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POLITECNICO DI TORINO

Corso di Laurea Magistrale

in Ingegneria Civile

Tesi di Laurea Magistrale

Freezing process in porous media

Relatori

Prof.ssa Marina Pirulli

Prof. Claudio Scavia

Candidato

Giorgia Amato

Anno Accademico 2018/2019

Contents

List of Tables iii

List of Figures iv

1 Introduction 1

2 Literature review 3

2.1 Frozen soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Freezing process in natural frozen soil . . . . . . . . . . . . . . . . . . . . . . . 5

2.3 Soil properties changes due to the freezing . . . . . . . . . . . . . . . . . . . . . 7

3 X-ray tomography for experimental geomechanic 13

3.1 X-rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.2 X-ray tomograph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.3 Images acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4 Tested soils and specimens preparation 21

4.1 Halden silt and Onsoy clay: Frost susceptible soils . . . . . . . . . . . . . . . . 21

4.2 Natural soil sampling and remolding procedures . . . . . . . . . . . . . . . . . . 23

4.3 Air bubbles detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5 Three-dimensional freezing processes 31

5.1 Topology of ice formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.2 Halden silt testing procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.3 Onsoy clay testing procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

i

5.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

6 One-dimentional freezing 43

6.1 Freezing chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6.2 Comparison between Halden silt and Onsoy clay . . . . . . . . . . . . . . . . . 45

6.3 Registration of images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6.4 Change in density over the time along the Onsoy clay specimen . . . . . . . . . 48

6.5 Deformations during the freezing process . . . . . . . . . . . . . . . . . . . . . 51

6.6 Validation of deformation analysis . . . . . . . . . . . . . . . . . . . . . . . . . 57

6.7 Further analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

7 Short-term deformations in 1D freezing 63

7.1 Brine melting point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

7.2 Image processing for 1D freezing analysis . . . . . . . . . . . . . . . . . . . . . 65

7.3 Influence of freezing temperature on clay deformation . . . . . . . . . . . . . . . 68

7.4 Freeze-thaw-freeze cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

8 Frost front penetration prediction 81

8.1 Stefan formula and Modified Berggren equation . . . . . . . . . . . . . . . . . . 81

8.2 Experimental data and model results comparison . . . . . . . . . . . . . . . . . 83

9 Conclusion 87

ii

List of Tables

4.1 Reconstituted specimen’s pores properties for Method 2, 3 and 4 . . . . . . . . . 30

5.1 Average ice lenses thickness for the fast freezing . . . . . . . . . . . . . . . . . 38

5.2 Average ice lenses thickness for the slow freezing, Experiment 1 . . . . . . . . . 39

5.3 Average ice lenses thickness for the slow freezing, Experiment 2 . . . . . . . . . 39

7.1 Mass of salt calculated to obtain -5, -10 and −22 ◦C melting temperature for 2.6

kg of water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

7.2 Summary of specimen physical characteristics for -5, -10 and −22 ◦C 1D freezing 73

8.1 Plastic index Ip, saturation degree S r, natural water content wn and dry densityt

γd measured for a clay sample by Kurz et al. (2017) . . . . . . . . . . . . . . . . 84

8.2 Frost front position after 700 min −12 ◦C freezing by Stefan formula and Modi-

fied Berggren equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

iii

List of Figures

2.1 Main types of cryostructures of mineral soils (ice is black) from Kanevskiy et al.

(2013) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Temperature profiles in Seasonally (left) and Perennially (right) frozen soil from

Andersland and Ladanyi (2004) . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3 Freezing process in one dimensional soil column from Nixon (1991) . . . . . . . 7

2.4 Typical X-ray radiograph and temperature profile from Akagawa (1988) . . . . . 8

2.5 3D image section views before and after freeze-thaw: a) longitudinal before, b)

horizontal before, c) longitudinal after and d) horizontal after from Wang et al.

(2017) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.6 Moisture content, void ratio and dry density variation along specimen height after

freeze-thaw experiments under four freezing temperatures from Wang et al. (2017) 11

2.7 Volumetric deformation vs. initial degree of saturation from Liu et al. (2019) . . 11

3.1 Change of trajectory of electrons due to the presence of a nucleus from Viggiani

(2018) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2 X-ray tube scheme from Ando (2006) . . . . . . . . . . . . . . . . . . . . . . . 15

3.3 Medical device for x-ray tomograph scans . . . . . . . . . . . . . . . . . . . . . 16

3.4 Medical tomograph’s scanning scheme form Love (2017) . . . . . . . . . . . . 16

3.5 3SR laboratory’s Tomograph from Ando (2006) . . . . . . . . . . . . . . . . . . 17

3.6 3SR tomograph’s scanning scheme from Wang et al. (2017) . . . . . . . . . . . . 17

3.7 Indirect detector scheme from Commons (2017) . . . . . . . . . . . . . . . . . . 18

3.8 Reconstruction of horizontal slices . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.9 Significant quantities for the spacial resolution . . . . . . . . . . . . . . . . . . . 20

iv

4.1 Frost-susceptibility of soil based on the grain size distribution curve from Slunga

and Saarelainen (2005) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.2 Grain size distribution of Halden Silt from Blaker et al. (2016) and Onsoy clay

from Muthing et al. (2017) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.3 Procedure 1: a. Slurry, b. Vacuum chamber, c. One-dimensional consolidation,

d. Kaolin clay reconstituted specimen . . . . . . . . . . . . . . . . . . . . . . . 25

4.4 Vertical section of reconstituted clay by Method 2 . . . . . . . . . . . . . . . . . 26



4.7 Procedure 4: a. Mixing, b. Casagrande apparatus, c. Concrete vibrator, d. Oe-

dometer consolidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.8 Number of air bubbles vs. diameter fo Methods 2,3 and 4 . . . . . . . . . . . . . 30

5.1 Horizontal section frozen specimen: a. fine Fontainebleau sand, b.bentonite clay

and c. kaolinite clay, d. density profiles shown across an ice lens in the kaolinite

specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5.2 Halden silt specimen’s horizontal and vertical section in unfrozen state for Freez-

ing 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.3 Halden silt specimen’s horizontal and vertical section in frozen state for Freezing 1 35

5.4 Halden silt specimen’s horizontal and vertical section in unfrozen state for Freez-

ing 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.5 Halden silt specimen’s horizontal and vertical section in frozen state for Freezing 2 37

5.6 Binarized horizontal section of frozen clay: a. before skeletonization and b. after

skeletonization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.7 Onsoy clay specimen’s horizontal and vertical section in unfrozen (left) and

frozen (right) state, −12 ◦C fast freezing . . . . . . . . . . . . . . . . . . . . . . 39

5.8 Onsoy clay specimen’s horizontal and vertical section in unfrozen (left) and

frozen (right) state, −12 ◦C fast freezing . . . . . . . . . . . . . . . . . . . . . . 40

5.9 Onsoy clay specimen’s horizontal and vertical section in unfrozen state, −20 ◦C

fast freezing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

v

5.10 Onsoy clay specimen’s horizontal and vertical section in frozen state, −20 ◦C fast

freezing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.11 Onsoy clay specimen’s vertical section for slow freezing (a: experiment 1 (w=61%),

b: experiment 1 (w=49.6%), c: experiment 2 (−5 ◦C), d: experiment 2 (T=−7 ◦C) 42

6.1 Water heating curve from Zumdahl and Zumdahl (2011) . . . . . . . . . . . . . 44

6.2 Freezing chamber adopted for the first experimental campaign . . . . . . . . . . 46

6.3 Freezing chamber adopted for the second experimental campaign . . . . . . . . . 47

6.4 Halden silt vertical section after 0 min . . . . . . . . . . . . . . . . . . . . . . . 48

6.5 Halden silt vertical section after 84 min . . . . . . . . . . . . . . . . . . . . . . 48

6.6 Halden silt vertical section after 162 min . . . . . . . . . . . . . . . . . . . . . . 49

6.7 Onsoy clay vertical section after 0 min . . . . . . . . . . . . . . . . . . . . . . . 49

6.8 Onsoy vertical section after 120 min . . . . . . . . . . . . . . . . . . . . . . . . 50

6.9 Onsoy vertical section after 204 min . . . . . . . . . . . . . . . . . . . . . . . . 50

6.10 Slice elevation (in pixels) for which change in density was computed . . . . . . . 52

6.11 Square extracted portion from 4D registered image . . . . . . . . . . . . . . . . 53

6.12 Mean of grey values over the time at elevation 150 pixel . . . . . . . . . . . . . 53





6.17 Mean of grey values over the time at elevation 650 pixels . . . . . . . . . . . . . 56

6.18 Mean of grey values along the specimen at the first x-ray scan . . . . . . . . . . 56

6.19 Mean of grey values along the specimen at the last x-ray scan . . . . . . . . . . . 56

6.20 Gray value of the relative maximum over the time . . . . . . . . . . . . . . . . . 57

6.21 Different zones identified along the specimen . . . . . . . . . . . . . . . . . . . 57

6.22 Axial elongation, change in volume and rigid vertical displacement over the time

within Zone 1, 2 and 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

6.23 Horizontal strains over the time within Zone 1, 2 and 3 . . . . . . . . . . . . . . 59

6.24 Cross section chosen at the bottom (left) and top (right) before freezing . . . . . 60

6.25 Cross section chosen at the bottom (left) and top (right) after freezing . . . . . . 61

vi

6.26 Rate of the mean of the grey value over the time (35 step of 6 min) . . . . . . . . 62

7.1 Onsoy clay vertical section (left) at the last recorded instat of thawing (right)

once the thawing was completely over . . . . . . . . . . . . . . . . . . . . . . . 67

7.2 Characteristic sections identified at the end of the −12 ◦C first 1D freezing . . . . 68

7.3 Characteristic sections identified at the end of the −12 ◦C second 1D freezing . . 68

7.4 Characteristic sections identified at the end of the −5 ◦C 1D freezing . . . . . . . 69

7.5 Characteristic sections identified at the end of the −22 ◦C 1D freezing . . . . . . 69

7.6 Top temperature over the time for −5 ◦C 1D freezing . . . . . . . . . . . . . . . 69



7.9 Mean of grey values over the time for -5, -12 and −22 ◦C 1D freezing and for

−22 ◦C second 1D freezing at the maximum frozen height . . . . . . . . . . . . . 71

7.10 Specimen initial and final height and frost front elevation for -5, -12 and −22 ◦C

1D freezing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

7.11 Maximum frozen height and freezing period obtained in this work . . . . . . . . 72

7.12 Maximum frozen height and freezing period from Wang et al. (2017) . . . . . . . 72

7.13 Frost front elevation over the time and freezing temperature for -5, -12 and

−22 ◦C and −12 ◦C second freezing . . . . . . . . . . . . . . . . . . . . . . . . . 74

7.14 Frost heave elevation over the time and freezing temperature for -5, -12 and

−22 ◦C and −12 ◦C second freezing . . . . . . . . . . . . . . . . . . . . . . . . . 74

7.15 Average ice lenses thickness for the three different 1D freezing processes . . . . 75

7.16 Specimen’s vertical section in unfrozen state . . . . . . . . . . . . . . . . . . . . 78

7.17 Specimen’s vertical section at the end of the first freezing . . . . . . . . . . . . . 78

7.18 Specimen’s vertical section at the end of the the thawing . . . . . . . . . . . . . 78

7.19 Specimen’s vertical section at the end of the second freezing . . . . . . . . . . . 78

7.20 Diameter along the height specimen for four different instant . . . . . . . . . . . 79

8.1 Correction coefficient in the modified Berggren formula from Aldrich Jr (1956) . 84

8.2 Frost front penetration over the time by Stefan equation for 0, -3, -4, −5 ◦C TP . 85

vii

Abstract

Frozen soil is a multi-phases system composed of mineral particles, ice, unfrozen water and gas.

Due to the existence of ice, several factors affect frozen soil properties (e.g., pressure, temper-

ature, salinity, etc..). Mechanical and deformation behaviour of frozen soil is not completely

clear. A better understanding of physical frozen soil properties and of its freezing process are

needed to improve the prediction of frozen soil deformation characteristics. This has application

in aged cold region engineering problems such as the Frost heave but also in new issues of the

modern era related to the Artificial Ground technique and to Global warming, since the recorded

increasing creep settlements. This thesis describes different freezing procedures to make a ele-

mentary representative frozen specimen. Its mechanical response corresponds to the mechanical

behaviour of soil only if the frozen specimen is homogeneous and isotropic and does not con-

tain ice segregation inside the soil matrix. If not, the mechanical response would be the sum of

that from ice and from frozen soil. Two kind of frost susceptible soil were investigated: Halden

silt and Onsoy clay. The Onsoy clay showed ice lensing phenomena, while Halden silt frozen

without the development of ice lenses. The analysis were computed on 3D images taken by the

x-ray tomography scanner. Further investigation were carrier out on the 1D freezing process.

Its evolution was scanned over the time by x-ray tomography. Moreover, this last allowed to

explore and analyze phenomena involved by freezing, such us frost heave and section shrinkage

for the clay. The frost heave and the maximum frozen height were measured for the 1D frozen

clay specimen at different thermal gradients. A reliable quantification of section shrinkage was

obtained by digital image processing of 3D images, taken during a one freeze-thaw-freeze cycle.

viii

Acknowledgments

Firstly I would like to thank Professor Gudmund R. Eiksund for teaching me all I needed to

work with frozen soil and carefully following me in every step. Many thanks to Dr. Edward

Ando for be present (physically and virtually) in every moments and for encouraging me to do

more and more. You taught me a lot about tomography and image processing and you showed

me how much passionate the research world is. A particular thank for Professor Cino Viggiani,

who believed in me and supported me in the worst moments. Thanks for your classes and life

lessons. Thank to Professor Alice Di Donna, for all the valuable advises she gave me during

these months. I would like to thank Professor Marina Pirulli and Professor Claudio Scavia for

being my supervisors at Politecnico of Turin. Un grazie speciale va alla mia famiglia. Grazie

mamma per non avermi mai fatto sentire sola ed essermi sempre stata vicina anche a kilometri di

distanza. Grazie per aver esultato insieme a me dopo le mie vittorie e avermi sostenuto quando

sono stata sconfitta. Conosci sempre la parola giusta da dire. Grazie papa per aver sempre

creduto in me e per avermi aiutato a valutare tutte le decisioni prese durante la mia carriera

universitaria e non. Tu mi hai insegnato ad osare e a non arrendersi mai di fronte agli ostacoli

che la vita pone davanti. Grazie a mio fratello Dario per essermi stato vicino e avermi sempre

fatta ridere. La tua voglia di fare e da sempre un esempio per me. Ringrazio Anna e Mariachiara,

le mie amiche di sempre. Grazie Stefania per il sostegno e l’affetto. Vorrei poi ringraziare tutti

i colleghi con cui ho avuto il piacere di collaborare durante il mio percorso di studi. Ciascuno

di voi mi trasmesso un insegnamento. In particolare grazie a Serena e Roberta, fedeli alleate

che l’universita mi ha regalato. Grazie alla mia Crazy Family, che durante quast’ultimo anno

mi e stata vicino. Ringrazio infine tutti gli zii, i cugini e gli amici che sono stati fonte continua di

energia durante questo percorso.

ix

Chapter 1

Introduction

Since the Cold-war era, engineering properties of frozen soils have been investigated. The first

research groups born to study permafrost and frozen materials, initially with military installation

purposes and then to develop the north Russia [Cole and Abdullahi (2001)].

Nowadays, many other issues bring civil engineers to further study frozen soils physical,

thermal and mechanical properties. On one hand, in frost susceptible soil frost heave causes the

raise of the ground, damaging pavements and structures’ foundations. On the other hand, over

the last years global warming is generating new foundation challenges. Due to the increasing

large-scale ground temperature, permafrost and seasonally frozen soil are getting more and more

warm, evidencing creep settlements of the ground and slope instabilities.

Furthermore, over last few decades, properties of frozen soil have been further explored to

improve new techniques, recently arisen in the scenario of the ground stabilization. First and

foremost, the Artificial Ground Freezing (AGF) provides the improvement of the soil strength

and get it impervious by extracting heat from soil.

Current researches aim to develop constitutive models able to describe the stress-strain behav-

ior of frozen soil. This is an hard challenge, since several factors need to be taken into account

(e.g., pressure, temperature, salinity, unfrozen water, etc..). Furthermore, many kind of cryogenic

structures exists in nature [Kanevskiy et al. (2013)].

When upon freezing, ice segregates inside the soil matrix, assuming different shapes and

making frozen soil inhomogeneous. In this conditions, mechanical tests’ responses would be the

sum of the response of two different phases, the frozen soil and the ice.

1

1 – Introduction

To obtain the actual behavior of frozen material, avoid the segregation of ice lenses in frozen

soil is needed. The main objective of this research is to study different freezing procedures in

order to find the parameters affecting the ice crystal size and identify the freezing procedure

which allows to get an elementary representative frozen samples. In this last, ice crystals are

expected to be uniformly distributed, in the way they cannot be identify as a separated phases

from frozen soil.

Further analysis were also carried out as an attempt to extend the understanding of the short-

term deformations. Indeed, despite of frozen soil has been studied for a long time, short and

long-term permanent changes in soil structures as a result of freezing are not well understood.

Furthermore, the demand of short-term volumetric changes prediction is increasing by the AGF

techniques. They require an accurate estimation of stresses involved on the surrounding soil by

the ground freezing to avoid damages on the near buildings and infrastructures.

Two frost susceptible soil were analyzed during this master research: the Halden silt and the

Onsoy clay. After a first examination of the clay sampling procedures, several specimens were

made.

Different three-dimensional freezing procedures were tested and then the understanding of

the freezing phenomenon was extended by the analysis of the one-dimensional freezing. Indeed,

if one looks at the phenomena at a smaller scale, even the three-dimensional freezing process

occurs due to a one dimensional thermal gradient.

Clay specimens were 1D frozen imposing three different thermal gradients. The deformation

behaviour of clay was observed also upon one freeze-thaw-freeze cycle.

Finally, the experimental data were compared with the results from two frost front penetration

models: the Stefan formula and the Modified Barggren equation, adopted by cold region civil

engineering for the frost front penetration prediction.

The analysis carried out in this master project were possible by using the digital image pro-

cessing of 3D images, scanned by the x-ray tomograph. This latter consists of a x-rays source,

which shots x-ray to the soil mass, and a detector, which measures the x-ray attenuation field due

to the material crossing. The peculiarity of x-ray tomography is that scans are taken from many

different angular positions. The reconstruction of these scans returns a 3D image. These latter

are composed of voxels (3D pixels). Each voxel returns a measurement of the x-ray attenuation

in terms of grey value, which is closely related to the mass density [Viggiani et al. (2014)].

2

Chapter 2

Literature review

This chapter presents an overview about frozen soil, natural freezing processes and the deforma-

tion mechanisms observed in literature. It wants to introduce sufficient background knowledge

for understanding the basic behavior of soil upon freezing.

2.1 Frozen soil

Natural frozen soil exits in large parts of northern Europe, north central Asia, Alaska, Canada,

southern part of south America and large parts of the United States, which are Cold regions, since

their isotherm is 0 ◦C in the coldest month of the year[Bates and Bilello (1966)]. Frozen soil is

defined as the soil with a temperature below 0 ◦C [Andersland and Ladanyi (2004)]. If the soil

keeps this last temperature during at least two consecutive winters and the intervening summer,

frozen ground is called Permafrost or Perennially frozen ground, while it is defined Seasonally

frozen soil or Active layer if its temperature fluctuates above and below 0 ◦C [Andersland and

Ladanyi (2004)].

In nature, frozen soil exists in the form of cyostructure, defined as a pattern formed by inclu-

sions and lenses of pore and segregated ice [Kanevskiy et al. (2013)]. Figure 2.1 shows the main

cryostructure types of mineral soils found in nature. In the upper permafrost of the Beaufort Sea

Coast of Alaska, Kanevskiy et al. (2013) found that the most common cryostructure of silt and

clay was the Ataxitic in which soil aggregates are suspended in an ice matrix.

Frozen soil mainly differs from the unfrozen soil since it contains ice in addition to the mineral

3

2 – Literature review

Figure 2.1: Main types of cryostructures of mineral soils (ice is black) from Kanevskiy et al.(2013)

particles, water and air or gas. Its constituents coexist and interact with each other and may switch

their phases, depending on the environmental changes [Jia (2018)]. The size and shape of soil

particles affects the molecular interaction forces of the mineral particles with each other and with

water. Inter molecular forces are able to suppress freezing although temperature drops below

0 ◦C.

Water exists in three states depending on its distance from the mineral particles. Firmly bond

water is called the first layer surrounding the mineral particle on which interactive forces are

higher. Such water does not freeze even if temperatures drops to −186 ◦C. The attractive forces

decreases on the next layer, which is called loosly water. Finally, Free water exists farther from

mineral particles and when temperature drops below the freezing point it is frozen first. Such

forces becomes bigger for large specific surfaces of the mineral particles. It is the case for clay

and silt. By cooling down sand and clay below the freezing point, the unfrozen water content

was measured from 0.2 to 2% and from 5 to 40%, respectively. Therefore, especially for the clay,

taking into account the existence of unfrozen water is needed, since it is massively present when

it is frozen [Tsytovich (1960)].

Ice is the main constituent which gets frozen soil of particular interest. Depending on the

micro structure of soil, pressures and salinity, ice does not form necessary at 0 ◦C [Fofonoff and

Millard Jr (1983)]. For cohesionless soils with small specific surface area, the initial freezing

4

2.2 – Freezing process in natural frozen soil

temperature T f can be close to 0 ◦C, while for cohesive soils soils T f can be −5 ◦C. Compar-

ing to the unfrozen soil, the existence of ice soil significantly increases the strength of frozen

soil [Andersland and Ladanyi (2004)] and decreases its permeability and deformability. On the

other hand, it makes the frozen soil’s behavior not easy to understand and predict, since it get

influenced by many factors, e.g., loading rate, temperature, pressure, salinity, etc.. [Jia (2018)].

2.2 Freezing process in natural frozen soil

The natural freezing process is a one-dimensional phenomenon leaded by a vertical thermal

gradient. In cold regions, due to the air temperature, ground surface reaches below 0 ◦C tem-

perature. This last increases moving down toward the Earth’s core, due to the geothermal heat.

Furthermore, geothermal heat makes the air temperature can’t affect the soil temperature below

10 or 20 m [Andersland and Ladanyi (2004)]. Temperature profiles in Seasonally and Perennially

frozen soil are shown in Figure 2.2.

Figure 2.2: Temperature profiles in Seasonally (left) and Perennially (right) frozen soil fromAndersland and Ladanyi (2004)

To model the cryogenic processes in permafrost and seasonally frozen soils, Thomas et al.

(2009) considered two seasonal freezing scenarios. The One-sided freezing, for soils without

permafrost, where frost front penetrates from the surface downward and the two-sided freezing,

5


for soils underlain by permafrost, where large thermal gradient above the permafrost layer can

make active layer freezing in two directions, from the permafrost table upwards and from the

ground surface downwards.

In his Discrete ice lens theory, Nixon (1991) modeled the one-side monodimensional freezing

process on a homogeneous fine-grained soil column (Figure 2.3). He identified a zone of frozen

soil, an active ice lens, a freezing fringe zone and an underlying zone of unfrozen soil. The active

ice lens grows by freezing unfrozen water existent at its boundary, which has gone through frozen

fringe. Since the freezing fringe are region of impeded flow caused by partial filling of soil pores

by ice, ice lens stops growing when the water supply of the current frozen fringe is cut off [Nixon

(1991)].

In the frozen fringe region, soil skeleton is assumed incomprehensible and it only expands

when the pressure in the ice exceeds the overburden pressure plus an additional pressure compo-

nent required to initiate the parcicle expantion [Nixon (1991)]. Pressure in the ice is due to the

volumetric expansion of water within the unfrozen pore of the frozen fringe, caused by the phase

change from liquid to ice (Miller (1972)).

During the freezing process, soil contains water in two phases: ice and liquid. Unfrozen water

is assumed always be located between the surface of the porous matrix and the ice. Under the

hypothesis of phase thermodynamic equilibrium, the equilibrium for the chemical potential of

the two phases results in the Clapeyron equation (Black (1995)):

Vwdpw − Vidpi =∆Hwi

T0dT (2.1)

in which V is the molar volum, p and T are absolute pressure and temperature for the phases

water w and ice i. ∆H is the molar heat of fusion at T0 (273.15 K).

In response to the thermal gradient, a pressure gradient is developed at the two phases inter-

face, defined as cryogenic suction. This last drives the pore water in the unfrozen soil towards

the freezing front.

On the bases of the Clapeyron equation and under the assumption of isotropic, homogeneous

and saturated soil, Thomas et al. (2009) expressed cryogenic suction (S T ), as:

S T = ρlLT − T0

T0(2.2)

in which ρl is the pore water density, L the latent heat of fusion, T is temperature and T0 is the

freezing point of pore water (both in Kelvin). Due to the water relocation, the soil below the

6

2.3 – Soil properties changes due to the freezing

Figure 2.3: Freezing process in one dimensional soil column from Nixon (1991)

frozen fringe zone undergoes consolidation, while positive vertical displacements are measured

near the surfaces [Jia (2018)].

2.3 Soil properties changes due to the freezing

Deformation mechanisms in soil upon frost have been analyzed over the years. A considerable

amount of researches have been carried out to understand the Frost heave mechanism. It is de-

fined as the upwards swelling of soil during freezing condition caused by an increasing presence

of ice as it grows towards the surface.

Frost heave results not just from the expansion of the water volume contained in the pores

but a supply in water has been observed, when a source of water is available. Furthermore, the

amount of surface heaving is found not proportional to the depth of freezing [Taber (1929)].

7


New techniques were developed in order to study frozen soil deformations. Akagawa (1988)

combined conventional frost heave test to X-ray radiography. In such occasion, the techniques

matching had a good response. X-ray radiography allowed to see differential expansion of soil

layers and ice crystals. A typical X-ray radiograph and temperature profile is visible in Figure

2.4. The width of expansion layer and the expansion rate decreased with time. Finally, between

the 0 ◦C isotherm and the expanding layer, a shrinking layer was observed, putting forward the

idea that the water content may not be at saturation in this zone.

Figure 2.4: Typical X-ray radiograph and temperature profile from Akagawa (1988)

After the soil is frozen, its structure experiences changes; e.g., Chamberlain and Gow (1979)

observed vertical shrinkage cracks (much like desiccation cracks), developed because of the large

negative pore water pressure that evolves during freezing.

Qualitative observation has been realized about the shrinkage of soil upon freezing. For

instance, Chamberlain (1989) observed that in normally consolidated or weakly overconsolidated

soils when the soil starts to freeze its volume does not increase but shrink. While, not shrinkage

was seen by Ji-Lin and Wei (2006) for the overconsolidated soil, although an expansion was

noted once the cold source gets removed.

Structural change and volumetric shrinkage due to freeze-thaw were investigated by Wang

et al. (2017), by scanning a saturated clay sample before and after freeze-thaw. The freezing

was applied in one-dimensional way. X-ray tomography scans were taken at a spacial resolution

8


of 0.0012 mm3. Figure 2.5 shows the sample’s section obtained after the reconstruction of the

scans. During such study, a radial shrinkage of the sample was observed in the top zone of the

sample after thawing. A portion at the warm end did not freeze during the experiment. On the

basis of the existing knowledge about the cryogenic suction at the freeze fringe, the observation

about the pore pressure decrease in the soil beneath the freezing fringe during freezing and the

evidence of fissure shape change due to the ice lens formation, the authors state that the cause

of the shrinkage is the moisture migration from the warm end to the freezing fringe. The water

content was measured after the freeze- thaw process at different elevations of the sample (100 mm

in height), for four freezing temperature (2.6) and they indicate a moisture migration from the

warm end to the cold end. A densification of the top zone was obtained. During the study the

temperature gradient was identified as the main factors controlling the amount of moisture in the

same type of soil. Finally, moisture migration was identified causing the radial shrinkage, but

not the volumetric one, since the clay was saturated and the system was closed.

As recently observed on unsaturated silty clay sample upon −10 ◦C three-dimensional freez-

ing by Liu et al. (2019), deformation mechanisms depends on the initial degree of saturation S r

of the soil. In particular, above 75 % S r soil swells, while if it is less soil shrinks (Figure 2.7).

9


Figure 2.5: 3D image section views before and after freeze-thaw: a) longitudinal before, b)horizontal before, c) longitudinal after and d) horizontal after from Wang et al. (2017)

10


Figure 2.6: Moisture content, void ratio and dry density variation along specimen height afterfreeze-thaw experiments under four freezing temperatures from Wang et al. (2017)

Figure 2.7: Volumetric deformation vs. initial degree of saturation from Liu et al. (2019)

11

Chapter 3

X-ray tomography for experimental

geomechanic

During the last two decades, x-ray tomography has been more and more required in experimental

geomechanics for the study of geomaterials. X-rays allowed to understand the failure mechanism

of soil and rocks and to understand how natural processes take place in soils. For instance,

tomography scans were taken to see the bean seed growth in sand and ice lenses in frozen soil

[Viggiani et al. (2014)]. Current study are investigating the roots development in soil using x-

rays. Furthermore, several information about the mechanical behavior of granular materials have

been obtained by combining x-rays and mechanical test for geomaterials.

3.1 X-rays

X-ray were discovered by the German physics professor Wilhelm Rontgen on November 8, 1895

[Stanton (1896)]. They are electromagnetic radiations that exist in a certain range of wavelength

and frequency values in the electromagnetic spectrum (λ = 0.01 ÷ 10 nm; f = 1016 ÷ 1020 Hz).

As every type of radiation, they consist of photons, which are individual packets of energy. X-

ray distinguish in soft and hard X-Rays depending on their energy level. Soft X-Rays have lower

energy and they can be easily absorbed (frequency range ≈ 1016 ÷ 1018 Hz; higher λ values),

whereas hard X-Rays have higher energy and penetrate matter much more easily (frequency

13

3 – X-ray tomography for experimental geomechanic

range ≈ 1018 ÷ 1020 Hz; lower λ values).

X-rays are generated by an x-ray tube. It is a vacuum tube and it contains a cathode and a

anode. The cathode correspond to a low atomic number metal (e.g., brass) and it is connected to

the high tension circuit. The anode is placed in the opposite side of the tube and it corresponds to

a high atomic number metal (e.g., tungsten). The cathode is heated and then it releases electrons

for thermoionic effect. The cloud of electrons are accelerated and as they hit the anode. The

collision transforms the kinematic energy into heat and x-rays [Wikipedia (2019)]. The scheme

of the x-ray tube is shown in Figure 3.2.

Two physical ways exist for producing x-rays [Viggiani (2018)]:

1. by change of orbit of electrons coming from electronic shell: the transition of the electrons

between shells produces x-rays photons;

2. by changing the speed of electrons (i.e., braking and change of trajectory). It happens when

electrons pass close to a nucleus or through a magnetic field. In these occasion electrons

are attracted so they lose a part of their energy, emitting x-ray photons (figure 3.1).

The main characteristics of an x-ray beam are:

1. Energy (eV): capacity to penetrate matter;

2. Intensity (photon/sec): photon flux;

3. Convergence (rad) : ray geometry;

4. Size (m)

Intensity, Convergence and Size of the beam affect the Brilliance, which is expressed in photon/sec,

per mm2 of the beam size, per mrad2 of the open angle and for band width of 0.1% of the energy

considered. The higher the brilliance, the more powerful the system [Viggiani (2018)].

3.2 X-ray tomograph

Since long time, the tomograph has been used as an non-invasive medical device used to visualize

anatomy of the human body and to investigate about the health of organs, bones and tissues. The

14

3.2 – X-ray tomograph

Figure 3.1: Change of trajectory of electrons due to the presence of a nucleus from Viggiani(2018)

Figure 3.2: X-ray tube scheme from Ando (2006)

patient needs to be lying on the bed while the scanner is turning around body, shooting x-rays at

the body zone to investigate (Figures 3.3 and 3.4).

The tomograph in 3SR laboratory (Figure 3.5) is used for experimental geomechanics and

it consist of a source and a detector which are fixed, while the body turns thanks to a turntable

(Figure 3.6).

The source contains the X-ray tube, which produces an x-rays cone-beam (see 3.1). The

15


Figure 3.3: Medical device for x-ray tomograph scans

Figure 3.4: Medical tomograph’s scanning scheme form Love (2017)

beam is shoot against the specimen and the detector measures the x-ray attenuation due to the

specimen crossing. The detector of 3SR laboratory’s tomograph is a flat-pannel devise, indirect

in type, marketed for medical use. It works using a similar technology of image sensors in digital

photography and video. Indirect detectors contain a layer of scintillator material, typically either

gadolinium oxysulfide or cesium iodide, which are able to convert the incoming photons (x-ray)

into light (Figure). An amorphous silicon detector array is directly behind the scintillator. It is

manufactured using a process very similar to that used to make LCD televisions and computer

16

3.2 – X-ray tomograph

Figure 3.5: 3SR laboratory’s Tomograph from Ando (2006)

Figure 3.6: 3SR tomograph’s scanning scheme from Wang et al. (2017)

monitors [Kump et al. (1998)]. The scheme of an indirect detector is shown in Figure 3.7.

Detector contains millions pixels and, similar to a digital camera’s image sensor chip, each

pixel also contains a photodiode which generates an electrical signal in proportion to the light

produced by the portion of scintillator layer in front of the pixel. The signals from the pho-

todiodes are amplified and encoded by additional electronics positioned at the edges or behind

the sensor array in order to produce an accurate and sensitive digital representation of the x-ray

image [Kotter and Langer (2002)].

17


Figure 3.7: Indirect detector scheme from Commons (2017)

3.3 Images acquisition

Tomography allows to have a three-dimensional image of an object, called Tomogram. Once

this image is obtained, the object scanned can be sectioned in whatever direction to look inside

it. The Tomogram is obtained by taking several radiographs of the object at different angular

positions. Indeed, during the scanning the specimens turns since the support, on which it is

placed, rotates. Knowing the specimen’s center of rotation, the horizontal sections (slices) of

the specimen are first reconstructed and then the whole volume is obtained by a slice by slice

reconstruction (Figure 3.8).

Detector measures an x-ray attenuation field due to the crossing of the object placed between

the source and the detector. X-ray photons may interact with the object’s matter through differ-

ent mechanisms (e.g., Compton Scattering, Refraction and Reflection, Pair Production, Raleigh

Scattering). For soils and the energy of x-ray radiation used, the overarching mechanism of in-

teraction of x-rays with the material is photoelectric absorption. In a photoelectric absorption

event, an x-ray photon is absorbed by an atom, which causes an electron to be ejected.

The absorbed photon’s quantity depends on the beam energy and on the material density and

it follows the the Beer-Lambert law:

I = I0e−µρx (3.1)

18

3.3 – Images acquisition

Figure 3.8: Reconstruction of horizontal slices

where I0 is the Intensity of the beam measure when nothing is in between the source and the

detector, µ is attenuation coefficient related to a given energy, ρ is the material density; x is the

length of the crossed object.

Before starting the test, the detector needs to be calibrated by measuring the term I0.

In terms of digital images, spatial resolution refers to the number of pixels utilized in con-

struction of the image. Images having higher spatial resolution are composed with a greater

number of pixels than those of lower spatial resolution [Kenneth et al. (2019)]. The spacial res-

olution is expressed in µm/pixel and it is chosen depending the specimen size. On the basis of

the X-ray Collimator aperture D, the distance between Collimator-Object L and the distance of

Object-Detector l (Figure 3.9), the spacial resolution could be changed following the formula-

tion:

d =l

L/D(3.2)

The detector has a fixed number of pixel of a certain size in µm, but its effective size can be

changed by translating the support, on which the specimen is placed, between the source and the

detector (Figure 3.5).

19


Figure 3.9: Significant quantities for the spacial resolution

The spot size depends on the power of the x-ray source. Smaller spot size is achieved by

reducing the power of the x-ray source. To have good images, once the beam’s intensity is

reduced, the exposure time for acquisition of radiographs needs to be increased in order to use

enough of the detector’s dynamic range [Ando (2006)].

20

Chapter 4

Tested soils and specimens

preparation

Materials used during this research project are Halden silt and Ønsoy clay. Since no enough

amount of natural soil was available to test the freezing processes planned in the experimen-

tal campaigns, reconstituted specimens were made. The analysis of freezing processes needs

specimens to be homogeneous and isotropic,then several reconstituting sample procedures were

tested, in order to find the one which returns the most uniform material.

4.1 Halden silt and Onsoy clay: Frost susceptible soils

Susceptible soil are defined by Atakol (1969) such us soil ”in which significant ice segregation

will occur when the requisite moisture and freezing conditions are present”. Several methods

were proposed to test and classify frost heave susceptibility of soils based on particle size, pore

size characteristics, mineralogy, hydraulic conductivity, moisture content and availability, den-

sity and freezing conditions [Chamberlain (1981)]. The ISSMGE Commitee in 1989 proposed

a classification of frost-susceptible soil based on the grain size distribution curve (Figure 4.1).

Following this classification, soil can be defined as frost susceptible (FS) if its grain size distri-

bution completely falls in the region 1 of the graph in Figure4.1, while they are not when it is in

regions 2, 3 and 4. Soils in region 1L have low susceptibility and particular attention should be

21

4 – Tested soils and specimens preparation

paid for the borderline cases ([Slunga and Saarelainen (2005)].

Halden silt and Onsoy clay are two Norwegian kind of soils, whose grain size distribution

curves are shown in Figure 4.2. The main part of such curves stands in region 1, hence they are

frost susceptible soils.

Figure 4.1: Frost-susceptibility of soil based on the grain size distribution curve from Slunga andSaarelainen (2005)

10−4 10−3 10−2 10−1 100

0

20

40

60

80

100

Grain size (mm)

Pass

ing

(%)

Halden siltOnsoy clay

Region 1 boundaryRegion 1L boundary

Figure 4.2: Grain size distribution of Halden Silt from Blaker et al. (2016) and Onsoy clay fromMuthing et al. (2017)

22

4.2 – Natural soil sampling and remolding procedures

4.2 Natural soil sampling and remolding procedures

Halden silt specimens were made by coring the material from a cylindrical block of silt extracted

in Norway. To compensate the slight drying due to the travel from Norway to France, the sample

was saturated back. Once cored, the specimen was place on a porous stone in contact with water

and left in this condition for 24 hours. In this way it retook water thanks to the capillarity raise.

In the case of Ønsoy clay, the material arrived in the shape of cylindrical disturbed samples and

cubic block. Due to the lack of enough natural clay specimen to realize the planned tests for the

experimental campaigns, artificial clay samples were made afterwards by remolding the natural

ones.

No Standard explains which is the best way to remould and make representative clay speci-

mens. In literature many procedures have been adopted and identified as good solution for the

clay in hand. Burland (1990) defined reconstituted clay as “one that has been thoroughly mixed

at a water content equal to or greater than the liquid limit wL”. De Sheeran and Rj (1971) suggest

to make homogeneous clay sample by use 2.5 times the liquid limit. Penumadu and Dean (2000)

prepared reconstituted sample by remoulding first intact material at a moisture content of 1.8

times the liquid limit with the addition of deionized water, then, once it has been de-aired, the

slurry is one-dimensional consolidated.

The main problem found following such procedures was the presence of air bubbles left in the

final sample after consolidation. Air bubbles are incorporated at the slurry during the mixing and

the pouring process. Air bubbles affects the freezing process since they corresponds a preferential

location for the initiation of ice segregation. Furthermore, recent study have revealed that water

can infiltrate into deeper soil through preferential pathways where air-filled macropores exist

at the time of freezing [Niu and Yang (2006)] The discovery of such inhomogeneities in the

specimen was made thanks to the use of the x-ray tomography scanner. Several trials were done

and a good procedure was found to obtain homogeneous clay specimens.

However, before freezing, in any cases reconstituted cylindrical specimens are placed be-

tween metal end caps and put in latex membrane and this two last are keep fixed by o-rings.

Membrane is used to get soil impervious while caps are of metal to allow the thermal flux and to

no affect the freezing. Specimen is introduced in membrane using triaxial cell mould. Once the

membrane is placed inside the mould and gets adherent to the metal by vacuum, the specimens

23


is carefully make slide into the membrane. Afterwards, specimen’s equipment is completed by

metal cups and o-rings.

In what follows, the different specimen reconstitution methods are explained.

1. A first trial was conducted on Kaolin clay powder. Demineralized water was added to the

powder in the ratio 1,5:1, the manually mixed slurry (Figure 4.3 a.) was then reversed into

the consolidometer (42mm in diameter) by a spoon and subjected to 42 hours vacuum (Fig-

ure 4.3 b.). Afterwards, the slurry was one-dimentionally consolidated at 60 kPa (Figure

4.3 c.). The water in the slurry could drain both from the top and the bottom of the con-

solidometer. The consolidation pressure was gradually increases in step during a period of

27 h until 60 kPa, following the step 5 kPa, 10 kPa, 15 kPa, 30 kPa and 60 kPa. For each

step the vertical pressure was increased when the pore over-pressure was totally dissipated,

i.e., after the vertical settlement at that step was over. As Figure 4.3 d. shows, after took the

sample out from the consolidometer the surface of the specimen appeared extremely rough

because of left cavities between soil and consolidometer’s wall.

2. In order to avoid a nonuniform surface and obtain smaller air babbles, some adjustments

were made for the second trial. The water content was increased from 1,5 to 1,8 the liq-

uid limit to get a less viscous slurry and this latter was squeezed into the consolidometer

(42mm in diameter) by sac a poche, so that air is not trapped between one scoop and the

following one. The vacuum step was skipped because considered not working due to the

high viscosity of the mixture. The vertical consolidation pressure was increased to 200 kPa,

following the step 20, 70, 100, 150, 200 kPa . After consolidation, the specimen surface

appeared less rough, but inside small air bubbles were still evident, as visible from the

sample’s vertical section shown in Figure 4.4, captured by x-ray tomography scanner.

3. Unlike Kaolin clay, Onsoy clay samples were not reconstituted from powder but start-

ing from natural clay. In this case water was added until an homogeneous paste was ob-

tained. The final water content of the mixture was w=57%, while its liquid limit was found

wL=65%. The consolidometer (70 mm in diameter) was filled by soil using palette knife,

taking care to create no voids in the specimen. This latter was then subjected to 96 hours

consolidation at 57 kPa (similar to the pressure at the sampling depth to the in-situ pres-

sure).

24


Figure 4.3: Procedure 1: a. Slurry, b. Vacuum chamber, c. One-dimensional consolidation, d.Kaolin clay reconstituted specimen

The final sample was 70 mm in diameter and 61 mm in high. In figure 4.5 is shown the

vertical section of the specimen, captured by x-ray tomography scanner. Several voids with

different sizes still exist inside the sample.

4. Finally, the best procedure to make clay samples, found and suggested in this research

25


Figure 4.4: Vertical section of reconstituted clay by Method 2


project, is the following one. An homogeneous mixture of a high viscous liquid (Figure 4.7

a.) is obtained by adding water until the water content is slightly above the liquid limit, i.e.,

when at the Casagrande apparatus (Figure 4.7 b.) the number of blows are a little less than

26



25 [Lambe (2006)]. By this time, the mixture can be put into the consolidometer using

spoon. Filter papers are placed at the bottom and at the top, once the mixture is ready

for being consolidated. The removing of air bubbles is achieved by the use of a concrete

vibrator (Figure 4.7 c.) moved around in the clay for a couple of minutes. Vibration make

the soil around the vibrator liquid, allowing then air bubbles to rise and escape from the

mixture. A good quality clay sample is so obtained after a one-dimensional consolidation

in oedometer, as shown in Figure 4.7 d. The water contents achieved by samples before

consolidation was between 67% and 72%. After 72 hours of one-dimentional consolidation

the water contents varied between 51% and 55%. The variation in achieved water content

was due to variable piston friction in the consolidometers used. An example of vertical

section of an Onsoy clay specimen obtained following such procedure is in Figure 4.6.

However, before freezing, the reconstituted cylindrical specimens are placed between metal

end caps and put in latex membrane and this two last are kept fixed by o-rings. The mem-

brane is used to separate the samples from the cooling liquid in the freezer, while the pur-

pose for the metal end caps is to provide a firm support for rings and to allow the thermal

flux, without affecting the freezing. The membrane is placed using a triaxial membrane

27


stretcher. Once the membrane is placed inside the mould and gets adherent to the mould

by vacuum, the specimens is carefully slid into the membrane. Afterwards, specimen’s

equipment is completed by metal cups and double o-rings.

Figure 4.7: Procedure 4: a. Mixing, b. Casagrande apparatus, c. Concrete vibrator, d. Oedometerconsolidation

28

4.3 – Air bubbles detection

4.3 Air bubbles detection

Computation of number and size of air bubbles inside specimens using the usual laboratory tools

is not simple, so the comparison among the different sampling procedures was realized by the

use of The Software for the Practical Analysis of Materials (SPAM). SPAM is a software made to

handle x-ray tomography data, having strongly application in the field of science material. With

its package of Python functions SPAM allows to compute full-field displacements and strain,

changes in volume, porosity fields and it offers many other functions which can be used for

mechanical applications [Int (2019)].

Detection of air bubbles was realized by implementing a code, already written in SPAM to

detect the particle size of granular materials. Once the 3D image are taken by x-ray tomograph

and upload in the code, it is prepared for the pores detection. First a threshold is applied in order

to isolate air bubble from the soil. The extreme values of the threshold were identifies on the basis

of gray value frequency of the image. Then, a cylindrical mask is applied on the image to delete

what is outside the specimen. The soil texture is identified, dilated and its gray value is imposed

equal to zero. In the resulting image pores are isolated. Then, the function watershed identify

each single pore and label it, returning the numbers of pores. Volume of pores is finally computed

by the function volumes, which count the number of voxels, whose each label is made of. The

background is labeled as well and its volume was identified and subtracted and the analysis.

Such technique is able to detect an object at minimum 2x2x2 voxels in size. On the assumption

of spherical air bubbles, as they commonly appear, it is possible to obtain the diameter of each

pore. Furthermore, knowing the total air volume (VV) and the sample’s volume (VTOT ), it is

possible to calculate the air bubble porosity as:

φ =VV

VTOT(4.1)

In Figure4.8 histograms show diameters and numbers of air bubbles inside the reconstituted

specimen obtained by Method 2, 3 and 4. For the different methods, table 4.1 shows the air bub-

bles porosity, the amount of air bubbles and their greater size (expressed in term of diameter).

Method 2 involves in specimens full of tiny air bubbles dispersed in the solid matrix. Despite

of for the Method 3 and 4 the specimen’s size is twice the previous one, the amount of pores

decreases respectively of 2 and 4 times. Method 3 involves in higher porosity and it globally

29


contains bigger air air bubbles than the other case. The best reconstituting procedure is so iden-

tified in the Method 4 since it leads to lower porosity and less amount of pores than the other

cases. All the tested in this project were carried out on specimens prepared by Method 4.

Table 4.1: Reconstituted specimen’s pores properties for Method 2, 3 and 4

Method Air bubbles porosity (%) Number of air bubbles Maximum diameter (mm)2 2,2 1100 4.13 7,7 559 25,24 1,1 273 7,4

Figure 4.8: Number of air bubbles vs. diameter fo Methods 2,3 and 4

30

Chapter 5

Three-dimensional freezing

processes

Mechanical tests on frozen soils are usually carried out on artificial frozen specimens. As we

have see in the literature review, frozen clay and silt soil naturally tend to segregate and get

dispersed into a matrix of ice. In this conditions, mechanical tests responses would be the sum

of the response of two different phases, the frozen soil and the ice. To obtain the actual behavior

of frozen material, avoid the existence of ice lenses is needed.

Literature presents many different ways in which the frost is applied on the unfrozen soil

before the test is run. Wang and Nishimura (2017) froze the specimen (reconstituted Kasaoka

Clay) at −15 ◦C for 12 hours and then changed the temperature to -2, -5 or −10 ◦C before the

triaxial compression tests. Before the creep test on loess, Xu et al. (2017) cooled the specimen

for 48 hours down to the testing temperature (-2, -4 , -5 and −7 ◦C). To investigate the strength

and deformation characteristics of frozen sandy soil, again Xu et al. (2011) decided to mono-

dimensional freeze the specimen quick from the top to the bottom under −30 ◦C, to avoid frost

heave and the specimens were considered completely frozen after 48 hours.

In the following sections three-dimensional freezing procedures are applied to Halden silt

and Onsoy clay natural and reconstituted specimens. Comparisons between the frozen and the

unfrozen state are done after taking x-ray tomography scans.

31

5 – Three-dimensional freezing processes

5.1 Topology of ice formation

The topology of ice formation during freezing was explored by Viggiani et al. (2014). They

applied air 24 h of air freezing at −18 ◦C on remolded samples of fine Fontainebleau sand, kaoli-

nite clay and bentonite clay. Kaolinite and bentonite specimens were prepared at initial water

contents equal to their liquid limits. Samples were prepared just putting the material into a Plex-

iglas cylinder, resulting in sample 80 mm in diameter and 110 mm in height. The samples were

frozen and then scanned at a spacial resolution of 50 µm/voxel. Figures 5.1 show the horizontal

section of the frozen samples. The sand specimen shows no evidence of ice segregation. Lenses

grew inward from the specimen boundary in the kaolinite specimen. The bentonite specimen

was massively crisscrossed by ice lenses. The density profile was computed across one of the ice

lens of the kaolinite clay specimen (Figure 5.1). It shows a relatively constant density in the soil

mass next to lenses. The absence of a density gradient in the soil close to lenses suggests that

cryogenic suction-driven consolidation has been completed and the scans were taken when the

samples were in steady-state equilibrium. Furthermore, it was found that the ice lens formation

is a three-dimensional phenomenon.

5.2 Halden silt testing procedures

Large thermal gradient in 3D freezing is considered leading to an in-homogeneous tensional

state. Temperature at the specimen surfaces decreases while the core keeps the initial one, then

voids could open between these two phases. In this section, to avoid the just described situation,

two gentle freezing procedures were applied on cored Halden silt specimens (Section ??).

A plastic container, full of refrigerant liquid with a freezing point of −30 ◦C, was used as

freezing chamber and the specimens (in cling foil wrapped) were cooled down in the following

ways:

1. The refrigerant liquid was preventively cooled down to −12 ◦C, specimen was then placed

into the container and the temperature of the whole system was kept at −12 ◦C by freezer

for 24 hours.

2. The specimen was placed into the container, where refrigerant liquid was at 12 ◦C, then the

whole system was cooled down to −12 ◦C by freezer for 24 hours.

32

5.3 – Onsoy clay testing procedures

Figure 5.1: Horizontal section frozen specimen: a. fine Fontainebleau sand, b.bentonite clay andc. kaolinite clay, d. density profiles shown across an ice lens in the kaolinite specimen

The tomography scans show no clearly visible ice crystals for the first case (Figures 5.2 and

5.3) , while thin ice lenses at the boundary appear in the second one (Figures 5.4 and 5.5). If the

first procedure seems to be preferable for experiments, the second one could be also adopted if

the core of the sample is used.

5.3 Onsoy clay testing procedures

Freezing processes applied to natural and remoulded Onsoy clay specimens can be divided in

fast and slow freezing.

Fast freezing was achieved by air freezing and it was imposed on natural disturbed samples

with 55% in water content. Two experiments were carried out:

33


Figure 5.2: Halden silt specimen’s horizontal and vertical section in unfrozen state for Freezing1

1. 24 hours air freezing at −12 ◦C;

2. 24 hours air freezing at −20 ◦C;

Before and after freezing, each specimen was scanned at a spacial resolution of 60 and 65

µm/voxel, respectively. Since scanning took almost 40 minutes, frozen specimens were placed

in isolation chamber(16 cm in diameter and 32 cm in height cylindrical container full of EPS

granulate) and then positioned between x-ray source and detector. Figures from 5.8 to 5.10 show

the vertical and horizontal sections of the 3D images.

Slow freezing to -5 and −7 ◦C was applied by using a container full of 30 liters of antifreeze

fluid as freezing chamber. In this latter case remoulded specimens by Method 4 were used. To

apply slow freezing, the specimen is previously chilled from ambient temperature to 5 ◦C to avoid

development of tensions at surface due to the large thermal gradient. Then, it is placed in the

center of the chamber and the refrigerant fluid temperature is decreased by freezer (T=−14 ◦C).

To keep homogeneous the fluid temperature during the experiment, heat flow was produced in

the following way. Five 1 liter bottles were introduced into the refrigerant liquid. Since they were

34

5.3 – Onsoy clay testing procedures

Figure 5.3: Halden silt specimen’s horizontal and vertical section in frozen state for Freezing 1

filled of brine with different freezing point (-0.5, -1, -1.5, -2, −2.5 ◦C), once temperature reached

the freezing point they start releasing energy to create its crystal lattice . Hence, heat convection

involves in homogenize the refrigerant fluid temperature and help to make three dimensional the

freezing process. Finally, sand was mixed to the brine, to avoid supercooling (”cool (a liquid)

below its freezing point without producing solidification or crystallization [House (1993)]) and

make the battles sink.

X-ray tomography scans were taken before and after freezing and at some intermediate freez-

ing temperatures, in same cases. As for the severe freezing, the sample is placed in the isolation

chamber, during the almost 40 minutes scanning.

Two experiments of slow freezing were carried out:

1. Two specimens were kept at 5 ◦C by refrigerator for 2 hours, then they were placed into the

freezing chamber at 0 ◦C initial temperature and cooled finally down from 5 ◦C to −5 ◦C in

21 hours and 35 minutes. X-ray tomography scans were taken at a spacial resolution of

60 µm/voxel, before and after freezing. One of these two was also 20 min scanned when

the liquid temperature was −2 ◦C and −3 ◦C after 3 hours and 45 minutes and 6 hours of

35


Figure 5.4: Halden silt specimen’s horizontal and vertical section in unfrozen state for Freezing2

cooling, respectively. During the scanning, the specimen was kept in the isolation chamber.

2. The specimen was first placed in 2 liters container filled with 5 ◦C antifreeze liquid for 1

hour and 10 minutes. Then, the whole system (sample plus container) was introduced into

the freezing chamber at initial temperature of −4 ◦C. X-ray tomography scans were taken

after 4 hours and 20 minutes, during which temperature was fluctuating between -4.0 and

−4.8 ◦C. A further tomography was applied after 22 hours and 45 minutes, when antifreeze

fluid was at −7 ◦C at the depth of the specimen, inside the freezing chamber.

5.4 Analysis

For Onsoy clay, the tomography scans (Figures 5.7-5.11) show freezing leads to soil segregation

and ice crystals growth. In order to compare the different freezing procedures, an approximated

measurement of the average of ice lenses thickness was realized by using the Software Fiji, built

for the scientific image processing and analysis. By applying a threshold to the frozen clay

3D images, ice gets isolated from soil, and in this way simple is detect the amount of pixels

36

5.4 – Analysis

Figure 5.5: Halden silt specimen’s horizontal and vertical section in frozen state for Freezing 2

contained in ice lenses by the stack histogram. By imposing the skeletonization of the stack, just

the skeleton (1 pixel in thickness line) of the ice lens is left. The histogram of the skeletonized

image gives us the numbers of black pixels contained in the new 3D image. The ratio between

the amount of pixels involved before and after the skeletonization corresponds to the average

of ice crystal thickness in pixel unit. The corespondent thickness in millimeters is obtained by

multiplying the ratio to pixel size in millimeters.

Ice crystals develops with different inclinations and towards different directions during the

freezing process. For this reason ice lensesare hard to isolate, identify and characterize. In the

3D images obtained for −20 ◦C fast freezing, ice lenses were more distinguishable since they

were thicker, as we will see later. In such occasion, it was possible to observe that ice grows

in the shape of planes, more or less extended, and its thickness could change depending of their

position within the specimen.

For such reasons, by using the skeletonization method, one does not pretend to compute the

ice planes thickness but just quantify an average of them. That is just to do the comparison

among the methods analysed within this master project.

37


Figure 5.6: Binarized horizontal section of frozen clay: a. before skeletonization and b. afterskeletonization

The results of the analysis are summarized in Tables 5.1, 5.2 and 5.3, together with the freez-

ing temperature and and the water content. In Table 5.1, water content is the one measured before

freezing, while in Tables 5.2 and 5.3, it was measured after thawing.

Table 5.1: Average ice lenses thickness for the fast freezing

T (◦C) w (%) Thickness (mm)-12 55 0.14-20 55 0.26

5.5 Results

Despite of in some permafrost zones, frozen silt and clay present soil segregation and visible ice

crystals, for the case in exam Halden silt did not reveal a strong tendency to segregate. Hence, it

can be concluded that a reliable mechanical response of an Halden silt frozen specimen could be

obtained by using almost any freezing procedure.

Ice crystals develop through Onsoy clay when the temperature drops below −4 ◦C and that

makes the specimen non-homogeneous and an-isotropic. In particular, from the image processing

of the 3D tomography scans, different parameters affecting the ice lenses average thickness were

identified. Table 5.1 show that low freezing temperature leads to thicker ice planes. The reason

38

5.5 – Results

Table 5.2: Average ice lenses thickness for the slow freezing, Experiment 1

T (◦C) w (%) Thickness (mm)-5 61 0.22-5 49.6 0.08

Table 5.3: Average ice lenses thickness for the slow freezing, Experiment 2

T (◦C) w (%) Thickness (mm)-4 48.4 0.16-7 48.4 0.19

Figure 5.7: Onsoy clay specimen’s horizontal and vertical section in unfrozen (left) and frozen(right) state, −12 ◦C fast freezing

could be that due to a larger thermal gradient, a greater suction pressure develops towards the

core of the sample. That makes clay segregate and consolidate while water supply ice lenses,

making them longer and thicker. Some authors use Clapeyron equation to model this pressure

(e.g., O’Neill and Miller (1985), Thomas et al. (2009)). Table 5.2 allows to notice that in the

case of less water content the ice lenses are thicker than in the other case. Again in Table 5.3 an

increase in thickness can be seen when the temperature descreases.

As regards the slow freezing procedures, the two experiments were realized at a different

39


Figure 5.8: Onsoy clay specimen’s horizontal and vertical section in unfrozen (left) and frozen(right) state, −12 ◦C fast freezing

Figure 5.9: Onsoy clay specimen’s horizontal and vertical section in unfrozen state, −20 ◦C fastfreezing

40

5.5 – Results

Figure 5.10: Onsoy clay specimen’s horizontal and vertical section in frozen state, −20 ◦C fastfreezing

freezing rate. It appears evident that, for specimens almost equal in water content, despite of the

higher temperature, the second experiment at a freezing temperature of −4 ◦C make ice lenses

thicker than in the first experiment carried out at a freezing temperature of −5 ◦C. Hence, the rate

of freezing needs to be take into account to make the frozen specimen homogeneous, as well as

thermal gradient and water content.

Among the freezing methods tested during this master thesis, the slow freezing from 0 to

−5 ◦C was identified as the best procedure to freeze, since it involves the most homogeneous soil

material, despite the existence of small ice crystals.

41


Figure 5.11: Onsoy clay specimen’s vertical section for slow freezing (a: experiment 1 (w=61%),b: experiment 1 (w=49.6%), c: experiment 2 (−5 ◦C), d: experiment 2 (T=−7 ◦C)

42

Chapter 6

One-dimentional freezing

Soils may contain dissolved salt in their pore water, due to the mineral composition of rocks from

which they were originated or to their position relative to salt water source. Indeed, soils are in

may cases sedimented in seawater. For instance, that is the case of marine clays in Scandinavia

and Canada currently above sea level due to the land heave after the last ice-age Salt affects

the soil physical, mechanical and thermal properties. It increases the freezing-point depression,

increases the unfrozen water content and results in a reduced frost susceptibility [Andersland

and Ladanyi (2004)]. For these reasons, freezing usually occurs in soils when temperature drops

some degrees below 0 ◦C. In such occasion, heat is extracted from soils and a thermal flux

develops from the higher to the lower temperature. Despite of a three-dimensional freezing is

applied on the specimen, if the phenomena is seen at a smaller scale, the freezing process occurs

due to a one dimensional thermal gradient. Furthermore, the natural freezing process is one-

dimensional in natural seasonally and perennially soils and sometimes also in artificial frozen

ground. Then, in order to understand how the freezing process involves in porous media, one-

dimensional freezing was applied in Onsoy clay and Halden silt specimen.

6.1 Freezing chambers

The studying of one-dimensional freezing needed two experimental campaigns. In order to scan

the freezing process in soils, a small freezing chamber was designed to fit inside the tomograph.

43

6 – One-dimentional freezing

The freezing chamber planned for the first campaign was successively improved during the sec-

ond set of experiments. Such chambers were designed to freeze the specimen by the contact with

frozen brine, i.e., a mixture of salt and water. The contact with a mass at a temperature less than

that of the specimen develops a heat flow towards the frost source. When the specimen tempera-

ture drops some degrees below zero, it starts to freeze. Once the temperature reaches the brine’s

melting point, the mixture start to melt. The phase changing occurs at a constant temperature,

as Figure 6.1 shows. During the plateau, the brine’s crystal lattice is disrupt by breaking the

hydrogen bonds and just when the brine is completely, the temperature begin to raise [Zumdahl

and Zumdahl (2011)]. The plan was to unidimensionally freeze the specimen from the bottom to

the top, during the brine’s melting period.

Figure 6.1: Water heating curve from Zumdahl and Zumdahl (2011)

The designed freezing chambers are described in what follow.

1. For the first campaign the freezing chamber (Figure 6.3) was constituted by one cylindrical

44

6.2 – Comparison between Halden silt and Onsoy clay

container (125 mm in diameter and 130 mm in height) filled by1 L frozen brine for the clay

and 2 L frozen brine for the silt with −12° as melting point. The container was isolated

by almost 4.5 L of Expanded Polystyrene Granulate (EPS) granules, placed in a bigger

cylindrical container (160 mm in diameter and 325 mm in height). The camber’s vertical

section is shown in Figure 6.3. The specimen was inside latex membrane and between

metal caps. The bottom metal cap was placed straight on ice, to obtain a good contact

to the freezing source. Due to the ice melting, the tomography scans show the specimen

moved downwards during the freezing. Such problems was fixed in the second chamber.

2. During the second campaign, the amount of brine was increased to 3 L to record a longer

freezing process. The container for brine was 180 mm in diameter and 200 mm in height.

In such container, an hollow pedestal was introduces and a metal plate was placed on it.

The plate was 10 mm in thickness. The specimen was placed on the metal plate, in order to

avoid the movement of the specimen during the 3D scans. The brine container was inside

a bigger bucket (310 mm in diameter and 330 mm in height) filled by EPS granules. The

EPS layer on the top of the specimen was almost 50 mm, smaller than the one at the lateral

surfaces to ensure a one-dimensional freezing. Thermocouples were placed to know the

temperature in the system during the freezing. The freezing chamber’s vertical sections are

shown in Figures 6.2 and 6.3.

6.2 Comparison between Halden silt and Onsoy clay

During the first experimental campaign, Halden silt and Onsoy clay were one-dimensional frozen

imposing at the specimen’s bottom a temperature of −12 ◦C. Onsoy clay was frozen and scanned

for 210 min, while Halden silt for 162 min. Figures from 6.4 to 6.9 show the vertical section of

the specimens scanned at a spacial resolution of 120 µm for three subsequent instants. The gray

value in the scans is an average of the x-ray attenuation occurred for 5 min.

In Halden silt, the scans show that the one-dimensional freezing involves in a frost front which

moves upwards. It can be identified since above it the material keep the same gray tone, while

below the frozen soil appears darker, because of its density is decreased. No ice lenses develop

during the freezing process.

45


Figure 6.2: Freezing chamber adopted for the first experimental campaign

On the other hand, in the Onsoy clay specimen, a net frost front is not distinguishable but

ice lenses appear growing upwards. In order to investigate what the freezing process involved in

the Onsoy clay, two analysis were realized. First the change in density over the time along the

vertical section of the specimen was computed. Then, some questions born in this analysis were

answered by the computation of deformations occurred during the freezing.

6.3 Registration of images

As described in the previous sections, the Onsoy clay scans showed a moving sample. Such

problem made very hard the image processing and then difficult the freezing process study. In

order to get the bottom cap in the same position for each image, the registration of the 3D images

was realized. Using the functions of SPAM, a code was implemented. First, the Transformation

Gradient Tensor Φ was computed between one image and the one taken at the instant zero. The

46

6.3 – Registration of images

Figure 6.3: Freezing chamber adopted for the second experimental campaign

4x4 Φ is ”deformation function” which contains the familiar 3x3 F in the top-left, known as

”displacement gradient” dudx . The Φ matrix provides the 3D transformation between the deformed

image and the reference one. Its terms correspond to the average of elongations computed along

three orthogonal axis and of distortions. Furthermore, it can be decomposed with a polar decom-

position into translations, a rotation matrix and a stretch tensor. The first two are rigid motions.

Φ =

Fzz Fzy Fzx tz

Fzy Fyy Fyx ty

Fxz Fxy Fxx tx

0 0 0 1

Φ matrix is computed by the function lucasKanade, it starts an iterative process in with the

gray values of pixels within the reference and the deformed images are compared until the best

matching is found, then the transformation parameters are returned. After the correlation, rigid

translation and rotation vectors were extracted from the Φ matrix. Once they were inverted, a

new Φ matrix, containing just these values, was computed and then applied to the image.

47


Figure 6.4: Halden silt vertical section after0 min


6.4 Change in density over the time along the Onsoy clay spec-

imen

The analysis of the change in density was realized by the use of the software Fiji. The soil’s

change in density during the freezing process was measured at six different heights as shown in

Figure 6.10, where 800 pixels (96 mm) is the total height of the image. The change in density is

expressed in terms of gray values. Higher gray values express a greater density, since they are

generated by a major x-ray attenuation. Using the software ImageJ (Fiji), once registered, the

images were concatenated and just a square (300x300 pix2 in size, i.e., 36x36 mm2, centered

in the image center) was extracted from the 4D image (Figure 6.11), in order to avoid boundary

noise. Once the horizontal section is chosen, the trend of the mean of its grey values is plotted

over time (Figures from 6.12 to 6.17).

Since 16 bit images were handled, grey values range is 0-65536.

Elevation h=150 pixels (18 mm) is in the darker zone, here density decreases until it becomes

constant after 132 min. At elevation h= 250 pixels (30 mm), a peak is visible. It represents the

48

6.4 – Change in density over the time along the Onsoy clay specimen


Figure 6.7: Onsoy clay vertical section after0 min

higher density ahead the ice lenses, due to the suction pressure. A densification can be seen also

at h= 350 pixels (42 mm) at the end of the scanned freezing process. In the upper zone, density

keeps quite constant until depth h=650 pixels (78 mm), where a decreasing in density is recorded.

Two first explanations may be:

1. it is an x-ray reconstruction artefact due to the density contrast between sample and cap;

2. such gray values belong to the metal cap at the first scans and at the soil at the end.

This latter hypothesis implies a vertical elongation of the specimen during the freezing process.

In this way four different zones were identified along the height of the specimen. From the

bottom to the top, they are:

1. dark zone: this zone develops in a second time. Two hypothesis could be done to explain

the reason of this darker gray value

(a) due to the heat extraction, just in a second time the specimen’s bottom zone soil

reaches the temperature of −12 ◦C. In such condition, this darker gray value could

49


Figure 6.8: Onsoy vertical section after120 min

Figure 6.9: Onsoy vertical section after204 min

be an average of further small ice crystals (not well visible at a spacial resolution of

60 µm);

(b) since the frozen brine is melting, the specimen drops into the water. The presence of

this latter around the specimen could contribute to the x-ray attenuation;

2. ice lenses zone: within this zone ice lenses develop upwards, driven by the thermal gradi-

ent;

3. suction zone: the soil appears denser because, ahead the ice lenses, suction pressure devel-

ops due to the thermal gradient;

4. the soil appears undisturbed by the freezing.

A further analysis of the change in density was concluded by the computation of the gray

values mean along the whole height of the sample over the time. In this case images were not

concatenated. For each 3D image, a parallelepiped with square cross section (300x300 pix2

in size, centered in the image center) was extracted. The gray values mean was automatically

50

6.5 – Deformations during the freezing process

calculated for each square cross section by the software and plotted against the section position

(slice) along the specimen height. Differently from the previous analysis, in which different

sections were considered, now the entire specimen height was taken into account. Figures 7.10

and 6.19 show the mean of grey values computed in the horizontal slices of the sample, at the first

and the last time step. In the horizontal axis, there are the number of slice from 0, the first section

at the bottom to 800, the last at the top. The distance between each slice is 140 µm. The first and

the last big peak represent the attenuation of the aluminum caps and, between these two, the gray

value belongs to the sample. By doing the comparison between the graphs at these two different

time steps, it is possible to notice that the gray value of the relative minimum, representative of

the darker zone, decreases during the time, confirming what seen in the previous analysis (Figure

6.16). Ahead the relative minimum, a small peak is identifiable. Such peak can be considered

representative of the suction zone. By the comparison between the two graphs, it is interesting

to notice that the peak moves upwards but keeping the same value during the freezing process

(Figure 6.20). That suggests that, in the graphs in Figure 6.14 for h = 350 pixels (42 mm) the

density increases due to the suction zone is moved at that section, at the end of the freezing

process.

At first glance, one may say that such results indicate that the suction pressure is constant

during the process. Then, since the temperature below the specimen was constant, the thermal

gradient and the suction pressure follow a linear law, as in the Clapeyron equation (2.1). Looking

more accurately, the slopes of the curve ahead the peak changes (Figure 6.21, indicating that the

zone interested by suction gets longer over the time, calling into question the linearity of temper-

ature and suction. Furthermore, a plateau develops between the relative minimum and maximum.

It represents the average of frozen soil and ice crystals gray value and it keeps constant during

the freezing process .

6.5 Deformations during the freezing process

Deformations of the Onsoy clay specimen during the one-dimensional freezing process was com-

puted running the function lucasKanade of SPAM. The function returns the 3D transformation

from the reference image (usually the one at the instant zero) to the new image, expressed by the

Φ matrix. The code was implemented on the registered images. Since during the 1D freezing

51


Figure 6.10: Slice elevation (in pixels) for which change in density was computed

four different zones were identified (see Section 6.4). The transformation was computed in such

zones by isolating them during the matching operated by lucasKanade. The limits between zones

1 and 2 and between zones 2 and 3, as well as between soil and metal caps, where recognized

with a precision of 5 slices ( less than 1 mm), since the material changes its appearance. Between

zone 3 and 4, no precise limit was identifiable. Furthermore, to make the iterations converge, the

length of the zones was increased. In particular, metal caps where added to zone 1 and zone 3

(Figure 6.21), since their contraction due to the thermal gradient is negligible respect to the soil

strain. Figure 6.22 shows the axial elongation, the change in volume ∆V and the rigid vertical

displacement computed for each zone. The axial elongation was computed by subtracting 1 from

Fzz. Under the hypothesis of large displacements, the change in volume ∆V was calculated as

the determinant of the 3x3 matrix extracted from the Φ matrix by removing the last row and

column. Such 3x3 matrix is known in literature as the Transformation Gradient Tensor F. The

rigid vertical displacement was straightly returned by the Φ matrix. The explanation of graphs is

52


Figure 6.11: Square extracted portion from 4D registered image

Figure 6.12: Mean of grey values over the time at elevation 150 pixel

realized for each zone in what follows.

1. In zone 1, a positive axial elongation is recorded until the minute 150, after which it unex-

pectedly becomes negative. The same trend and almost the same values are shown by the

change in volume. Then, the change in cross section size is expected to be negligible, as

53




graphs confirm in Figure 6.23. Small vertical displacements were recorded. In particular

a maximum downwards displacement of 0.24 mm is recorded, confirming that the images

were well registered. No reasonable physical explanation are given for the contraction at

the end of the freezing.

2. Contrary to the zone below, in zone 2, a vertical contraction is recorded at the beginning

of the freezing process followed by a vertical expansion. Here, contraction could be due

to the effect of suction pressure while the zone starts to elongate when it is reached by ice

lenses. The same behavior is shown by the change in volume but with larger percentage

at the contraction time and lower percentage at the expansion time. Such observations

54




tell that horizontal strain is negative over the time. The maximum recorded expansion in

volume is almost 8%. At the end of the freezing, the entire zone is subjected to a vertical

upwards displacement of 11 pixels. Since the images were preventive registered, movement

at the basis of the sample was removed. Then, rigid displacement could only derive from

the integration of the axial elongation measured in the zones below, but actually it is not.

Furthermore, vertical displacement occur in the first 150 min of freezing, after that it keeps

constant.

3. Within the Zone 3, strains along the three axes and change in volume are negligible, while

the rigid vertical displacement is almost 10 pixels at the end of the freezing.

55


Figure 6.17: Mean of grey values over the time at elevation 650 pixels

Figure 6.18: Mean of grey values along the specimen at the first x-ray scan

Figure 6.19: Mean of grey values along the specimen at the last x-ray scan

56

6.6 – Validation of deformation analysis

Figure 6.20: Gray value of the relative maximum over the time

Figure 6.21: Different zones identified along the specimen

6.6 Validation of deformation analysis

As seen in the previous sections, the freezing process involves the change in density of the

material and the growing of new elements into the soil, i.e., the ice lenses. Such factors make

57


Figure 6.22: Axial elongation, change in volume and rigid vertical displacement over the timewithin Zone 1, 2 and 3

58

6.6 – Validation of deformation analysis

Figure 6.23: Horizontal strains over the time within Zone 1, 2 and 3

the correlation process difficult since the matching is searched between pixels whose gray value

changes. A validation protocol was thought to prove the results were reliable. The objective was

to test if the same vertical elongation is obtained, by calculating it in two different ways:

1. Manually: the 3D images taken at the beginning and the end of the freezing process were

considered. The same cross sections were identified at the bottom and the top of the speci-

men in the two 3D images (Figures 6.24 and 6.25). The difference of the distance between

the two cross sections at the beginning and at the end of the freezing process, gives the

vertical elongation, once it is multiplied by the pixel size. Such elongation was found equal

to 1.96 mm.

2. Axial strain: the component Fzz was extracted for each zone at the freezing end instant. By

59


multiplying such term by the initial height of the relative zone, its final height is computed.

The subtraction between final and initial eight returns the vertical elongation.

(a) first zone: δ = (1- Fzz) · h = (1 - 0.94) · ((196-163) · 0.14) = -0.28 mm

(b) second zone: δ = (1- Fzz) · h = (1 - 1.12) · ((330-196) · 0.14) = 2.25 mm

(c) third zone: δ = (1- Fzz) · h = (1 - 0.00) · ((661-330) · 0.14) = 0.00 mm

The sum of the vertical elongation occurred in the three zones returns a total elongation of

about 1.97 mm.

Elongations obtained in these two ways differ of 0.01 mm, which is enough small to say that

correlation works well, despite of the freezing process.

Figure 6.24: Cross section chosen at the bottom (left) and top (right) before freezing

6.7 Further analysis

The deformation analysis allows to confirm that specimen subjected to 1D freezing elongate.

Then, hypothesis (1) may considered confirmed about the change in density at the slice 650 (see

Section 6.4). Further analysis were realized about the dark zone, since it does not develop during

60

6.7 – Further analysis

Figure 6.25: Cross section chosen at the bottom (left) and top (right) after freezing

the 1D freezing processes, proposed in the following chapter. First the minimum gray value

within this zone was computed for each 3D image taken during the freezing. Such values were

plotted against the time (Figure 6.26). The slope of the curve changes over the time. In particular,

the gray value rate decreases in the first 15 time step, after which it increases from about α1 =

320 gray values/step to α2 = 420 gray values/step and then decreases again. Such result suggests

that the gray value in the dark zone is influenced by the sinking of the specimen into the brine.

Brine at −12 ◦C got in contact to the later surface of the sample. Furthermore, as it is visible from

Figure 6.9, in the dark zone region, outside the specimen, the background becomes less dark. It

suggests that the EPS granulates are wet.

61


Figure 6.26: Rate of the mean of the grey value over the time (35 step of 6 min)

62

Chapter 7

Short-term deformations in 1D

freezing

In permafrost or in seasonally frozen soil, temperatures usually does not drop below −5 ◦C.

Contrary, lower temperatures are imposed to stabilize soil or get it impervious by the Artificial

Ground Freezing (AGF). In this case, if the Liquid Brine System is adopted, brine circulates

in pipes with temperature between −25 ◦C and −30 ◦C , while soil temperature drops below

−80 ◦C when a Liquid Nitrogen System is installed [Chang and Lacy (2008)]. The design of

Ground Freezing System needs to predict the short-term volumetric change of soil, in order to

quantify the applied stresses on the surrounding soil and avoid damages on the near buildings

and structures. Furthermore, available methods to accurate estimate the thaw settlement after the

Ground Freezing are not been developed yet. As an attempt to increase the knowledge regarding

these issues, analysis were carried out to extend the understanding of these phenomena and to

increase data and information, which are critical for a good coupled thermal-hydro-mechanical

analysis.

The experiments were performed on clay specimen whose deformation effects were pro-

nounced during freezing, as seen in the previous chapter and by using the chamber 2 as freezing

chamber, as described in Section 6.1. The frost penetration and heave is first analyzed for dif-

ferent bottom freezing temperature, then the clay’s behavior is examined under one freeze-thaw-

freeze cycle.

63

7 – Short-term deformations in 1D freezing

7.1 Brine melting point

In order to obtain a specific bottom temperature, a review about colligative properties was real-

ized. Such properties depend just on the number of solute particles dissolved in the solution and

not on their chemical nature [Pasquetto and Patrone (1994)]. Among these, Freezing point de-

pression is a colligative property observed in solutions that results from the introduction of solute

molecules to a solvent. The freezing points of solutions are all lower than that of the pure solvent

and is directly proportional to the molality of the solution m. The molality corresponds to the

number of moles of solute per kilogram solven [Atkins and De Paula (2009)]. The proportional-

ity constant is called cryoscopic constant and it depends on the nature of the solvent, which for

water corresponds to Kcr=1.853 Kkg/mol. The freezing point depression was computed using

the formulation:

∆Tb = imKcr (7.1)

where i is the number of salt’s ions dissociated in the solution.

Once the solute is chosen to mix with water and the freezing depression is fixed, the grams of

salt can be calculated.

For the experimental campaign, NaCl salt was added to water. Since it was bought as com-

monly salt to cook, it was not pure. It contained some anti floucculant agents which made it

difficult to obtain a perfect prediction of the solution melting point.

Calculation of the salt amount on the basis of molality is no more valid when a freezing

depression to the Eutectic point is asked. The Eutectic temperature is the lowest possible melting

temperature of a solution. Sodium chloride and water form a eutectoid when the mixture is

23.3% salt by mass with a eutectic point at −21.2 ◦C.

In the following table, the amount of salt to add to 2.6 kg of water, to obtain -5, -10 and

−21 ◦C is shown. For the case of −10 ◦C and −21 ◦C the actual recorded melting temperature

were −12 ◦C and −22 ◦C, respectively.

Table 7.1: Mass of salt calculated to obtain -5, -10 and −22 ◦C melting temperature for 2.6 kg ofwater

T (◦C) -5 -10 -22Salt mass (g) 200 400 600

64

7.2 – Image processing for 1D freezing analysis

7.2 Image processing for 1D freezing analysis

Results about 1D freezing were obtained just after the 3D x-ray scans processing. In such sec-

tion, they are explained the procedures adopted to quantify the freezing period, the frost front

and the frost heave. The scanning of 1D freezing process was done for three different bottom

temperature: -5, -12 and −22 ◦C. For the −5 ◦C freezing the process was recorded until some

hours after the sample started thawing. For the −12 ◦C freezing, the scanning was extended for

a second freezing and stopped when sample started to thaw. Furthermore, for this case a second

freezing was done after the sample got completely melted. Due to scheduling reasons, the third

freezing process was scanned for just 6 h and 30 min.

For each bottom temperature case, series of scans with 6 min interval were conducted. The

time of x-ray scan was 5 min, while between two scans 1 min was spent to store the data. The

scanning was realized at a spacial resolution of 120 µm. Each set of scans was manually re-

constructed by using the software XACT and then joined a in 3D image (stack). For each 1D

freezing, several stacks were obtained and sorted in ascending order form 0, the first.

The freezing period was identified as the time from the start of freezing and the start of

thawing. The beginning of thawing was associated to the moment in which frost front started to

go downward. Furthermore, it was noticed such moment corresponds to the relative minimum

temperature recorded at the top of the sample (Figures 7.6 and 7.7).

By a first visual observation of the consecutive 3D images, the last stack before the thawing

started was identified. Then, for the 1D freezing at −12 ◦C, a range of about 30 stacks was

chosen, placing in the middle the approximated freezing end. Since the other freezing processes

were scanned for less time, all the stacks were considered. For each case the 3D images were

concatenated to create a 4D image. For the stack approximately identified as freezing end, the

frost height was detected and identified as the height in which ice lenses are no longer visible.

Once obtained the 4D image, all the horizontal sections was cropped by a square cross section

with size 36x36 mm2. The part of the image, which was outside the square, was removed to avoid

boundary noise.

The mean of the grey scale values was calculated as an average among the grey values in the

square and then plotted against the time. First, the grey value trend over the time was plotted at

the maximum frost front height. Since no much changes in density were visible at that height,

65


the grey values were plotted for the fourth slice below the frost front, i.e., 0.5 mm down.

Following such procedures, the graph in Figure 7.9 were obtained.

As discussed in Chapter 6, the soil is subjected first to suction and then it is crossed by ice

lenses. As the thawing starts, the frost front starts dropping and density increases again. For

this reason a relative minimum is expected in the graph of grey mean value against time. The

relative minimum marks the end of the freezing period. In Figures 7.9, the graphs of change in

grey values over the time for -5, -12 and −22 ◦C as bottom temperature are shown.

For the freeze-thaw-freeze (T=−12 ◦C ), the followed procedure was that above, but changes

were made in the vertical position of the slice considered for measure the grey value. At the

end of the second freezing, at the frost front ice lenses were more pronounced along the sample

edges. Moving the 36x36 mm2 square to the ages means incorporating grey values outside the

sample, which would invalid the measurement.

The problem was solved by keeping the 36x36 mm2 square in the center but moving it below.

The section in which ice lenses are no longer existent was found and the 36x36 mm2 square was

moved to the fourth slide down, i.e., to 0.5 mm down.

The detection of the thawing end was simpler than of end of freezing. Indeed, once the first

freezing was over, the scanning interval was increased from 6 min to 16 min. Then, the last 3D

image in which ice was still existent was easy identified. In Figure 7.1 are shown the vertical

section observed at the last recorded instat of thawing and the one recorded once the thawing was

completely over.

In the case of −22 ◦C, the scans were interrupted after 6 h and 30 min. As shown in Figure 7.9,

no relative minimum was detectable and then the freezing period was not over after that time.

Despite this, the identification of the freezing period was possible thanks to the data recorded

by thermocouples during the whole process. For each 1D freezing case, 6 thermocouples were

placed in different position of the freezing chamber.

For all the freezing processes analysed, but for the −22 ◦C case , the comparison among the

freezing period and temperatures developments shows that the end of freezing period corresponds

to the relative minimum of the temperature recorded at the specimen top. For this reason, it is

assumed that the same thing happens for the 1D freezing at lower temperature. This allowed for

identification of the time for maximum heigth of the frozen zone.

A spike can be seen in 7.8 for the −22 ◦C freezing due to the thermocouples re-positioning.

66

7.2 – Image processing for 1D freezing analysis

Figure 7.1: Onsoy clay vertical section (left) at the last recorded instat of thawing (right) oncethe thawing was completely over

In Software ImageJ (Fiji), the height of the frozen zone was identified by the last position

of the horizontal section in which ice lenses were visible. Due to presence of aluminum caps

and the density contrast between sample and cap, an x-ray reconstruction artefact exists at the

interface between soil and caps. The height of the specimen was considered at to the beginning

of such metal caps, which was identified as the first (closer to the soil) slice in which grey values

of metal caps are homogeneous and it was marked as end of the specimen. Figures from 7.2

to 7.5 show the characteristic sections identified at the end of each freezing process. Final frost

heave was calculated as the difference of the height of the specimen before freezing and at the

end of the freezing period.

Furthermore, frost heave was computed over the time by extracting the axial elongation from

the Φ matrix (see 6.3) calculated between the new image and the reference one during freezing

by Digital Image Correlation (DIC). It’s trend over the time is shown in Figures 7.14 for the

different bottom temperatures.

67


Figure 7.2: Characteristic sections identifiedat the end of the −12 ◦C first 1D freezing

Figure 7.3: Characteristic sections identifiedat the end of the −12 ◦C second 1D freezing

7.3 Influence of freezing temperature on clay deformation

As shown in Section 5.5, the freezing temperature, or the thermal gradient, affects the ice lenses

size. Contrary to the three-dimensional freezing presented in Chapter 5, the thermal gradient is

now nearly uni-directional. This allows to deeper investigate the freezing process and extract

further information about frozen soil characteristics. In table 7.2 and in Figure 7.10 are shown

the results obtained from the analysis in Section 7.2.

Wang et al. (2017) uni-diretional froze unsaturated clay specimen to -5, -7, -10, −15 ◦C. They

found that for lower bottom temperatures the maximum frozen height gets longer and thermal

equilibrium is reached later (Figure 7.12). Furthermore, they observed that as the temperature

within the specimen stabilized during the freezing process, the specimen reached a maximum

height (frost heave). At thermal equilibrium, the maximum frozen height was assessed based on

the temperature distribution and interpolation.

Also for the current case, the maximum frozen height is longer for lower freezing temperature

as shown in Figure 7.11. Contrary to the previous case, measurements were done on the basis

68

7.3 – Influence of freezing temperature on clay deformation

Figure 7.4: Characteristic sections identifiedat the end of the −5 ◦C 1D freezing

Figure 7.5: Characteristic sections identifiedat the end of the −22 ◦C 1D freezing

Figure 7.6: Top temperature over the time for −5 ◦C 1D freezing

of tomography scans processing. Image processing is considered to be an accurate and non

destructive way to detect the frost front, since the freezing temperature of water in the soil is not

easy to precisely estimate. Indeed, it depends on the salt which is dissolved inside it and on the

69




interactive forces with granular particles. At the freezing end, frost heave was measured equal

to 4.1% for−5 ◦C after 14 h freezing and 10% for both −12 ◦C and −22 ◦C after 13 h and 6 h and

30 min freezing, respectively.

As shown in Figure 7.11, the freezing period (time between the freezing and the thawing

beginning) was longer when brine melting temperature was −22 ◦C (17 h) and almost similar for

the −12 ◦C and −5 ◦C cases (14 h and 13 h, respectively). Such dissimilarities in freezing period

could be due to brine latent heat. Contrary to pure ice water, whose latent heat of melting is

almost constant for starting temperature, for a water-NaCl solution, Han et al. (2006) found that

70


Figure 7.9: Mean of grey values over the time for -5, -12 and −22 ◦C 1D freezing and for −22 ◦Csecond 1D freezing at the maximum frozen height

−20 −15 −10 −5

30

40

50

60

70

80

Temperature (◦C)

Hei

ght(

mm

)

Initial heightFinal height

Frost front elevation

Figure 7.10: Specimen initial and final height and frost front elevation for -5, -12 and −22 ◦C 1Dfreezing

it depends on the concentration of salt in water.

As recorded by thermocouples, after a short period in which brine temperature was constant,

it started to increase despite of not all the frozen brine got melted. That because a not perfect

insulation system was adopted. In particular, in the case of brine melting point of -12 and −22 ◦C,

71


Figure 7.11: Maximum frozen height and freezing period obtained in this work

Figure 7.12: Maximum frozen height and freezing period from Wang et al. (2017)

temperature was constant for almost the first 500 min, then it started to increases with a rate of

about 0.40 ◦C/h. While the −5 ◦C bottom temperature increased from the first instant with about

72


0.25 ◦C/h rate. For such reasons, despite of the purpose for such measurements was to detect the

freeze equilibrium time, they can give only an idea about how long was the specimen freezing.

Table 7.2: Summary of specimen physical characteristics for -5, -10 and −22 ◦C 1D freezing

T (◦C) -5 -10 -22Water content (%) 56 51 55

Freezing period (hours) 13 13.5 17Initial height H (mm) 70 70 71Final height HF (mm) 73 77 78*

Frost heave (mm) 3 7 8*Frost front elevation hF (mm) 30 57 62*

Frost heave (%) 4.3 10 9.9*? measured after 6 h and 30 min from the freezing beginning.

Frost front position over the time was measured in the 3D images every hour from the freezing

beginning until its end (start of thawing). It was identified as the last horizontal section, counting

from below, in which they ice lenses appeared. The development is shown over the time in

Figure 7.13 for -5, -10 and −22 ◦C 1D freezing. For the first minutes of freezing the slope of all

the curves is almost equal. Then, the freezing rate is slowing down for all the cases. For the −5 ◦C

freezing, frost front appears stable after almost 750 min, indicating that a steady state situation

was reached. The same thing was not observed for the other 1D freezing, since a plateau is not

identified for such cases.

Frost heave over the time was computed over the time as explained in Section 7.2. Figure

7.14 shows the graphs obtained for -5, -10 and −22 ◦C 1D freezing. By comparing the first 400

minutes for each 1D process, once can say that frost heave occurs faster at lower temperature.

For the -12 and −22 ◦C cases, it follows a curved trend with reduction in inclination, while for the

−5 ◦C case it appears more linear. Then, contrary to the first cases in which frost heave seems be

over in the first 500 min, for the −5 ◦C case it occurs more slowly and with almost the same speed

for longer time. For the case of −12 ◦C, maximum frost heave was measured almost 9% after

550 min by DIC, while at the end of the freezing process it was manually measured almost equal

to 10%. Such changes is due to the fact that between about 450 and 750 min, the function did not

converged before 100 iterations. For the other cases, the two kind of measurements correspond.

Comparing frost front propagation and frost heave trend over the time for −22 ◦C case, it is

seen that the frost heave shows the tendency to stabilize at 400 min while frost front looks like

73


Figure 7.13: Frost front elevation over the time and freezing temperature for -5, -12 and −22 ◦Cand −12 ◦C second freezing

Figure 7.14: Frost heave elevation over the time and freezing temperature for -5, -12 and −22 ◦Cand −12 ◦C second freezing

propagate with a speed of 10 mm/h. A similar behavior is shown by the −12 ◦C freezing. Indeed,

in this later case at about 500 min, the frost heave slope is starting to decrease, while frost front

continues to propagate. Such behavior is not evident −5 ◦C freezing.

74

7.4 – Freeze-thaw-freeze cycle

Further comparisons of the different freezing cases can be done in terms of average of ice

lenses thickness. Average ice lenses thickness was computed using the technique explained in

Section 5.4. Figure 7.15 shows that ice lenses thickness gets thinner with lower bottom temper-

ature. Surely, as seen in Chapter 5, an accurate comparison can be realized taking into account

the water content and rate of freezing.

−20 −15 −10 −5

0.3

0.35

0.4

0.45

Temperature (◦C)

Ice

lens

esth

ickn

ess

(mm

)

Figure 7.15: Average ice lenses thickness for the three different 1D freezing processes

7.4 Freeze-thaw-freeze cycle

A freeze-thaw-freeze cycle was performed on one clay sample. The first freezing was at −12 ◦C

and the second at −13.5 ◦C, since the brine mixture used in the second freezing had a slightly

lower melting point.

Contrary to what seen in literature (e.g., Wang et al. (2017)), the thawing was slowly, keeping

the melting brine below the specimen.

The period of the first freezing was measured 13.5 h. Thawing took 14 h and the second

freezing period (12.5 h) was recorded 1 h shorter than the first one.

Figures from 7.16 to 7.19 show the vertical section of the same sample in unfrozen state, after

the first and second freezinf and after the thawing. Figure 7.18 shows that the freezing causes

damage in the soil’s structure, leaving almost vertical cracks after the thawing. These cracks

could be the reason for the increase in permeability measured by Chamberlain and Gow (1979)

75


after a freeze-thaw cycle. After the thawing, water appear trapped between the sample and the

membrane, showing that water leaks out from the clay during the thawing. As we have seen in

Chapter 3, freezing process involves a redistribution of the water throw out the sample. Due to

the cryogenic suction, the water goes downwards, causing the densification of the top part while

the bottom zone becomes softer. Due to such redistribution, a certain amount of water passes

from a bond with particles state to a free state. As Tommik (2017) observed, when clay thaws

new bonds between particles are formed. Thawed clay sticks together forming larger particles.

Increasing particle size will decrease the specific surface area and therefore the amount of water

that can be bound to that area will also decrease. Then, new cracks and more amount of free

water, together with a slight decrease in temperature, might lead to a faster freezing.

The frost front was tracked during the first and the second freezing. The sample height was

also measured from the 3D images. As shown in Figure 7.13, frost front initially propagates at

similar speed. Then, the second freezing frost front keeps an higher speed than the first one, after

which it drastically decreases, keeping the frost front an almost stable position for 300 min.

The frost heave was measured for both freezing cases, once the freezing period was over. As

shown in Table 7.2 , it is measured equal to 10% for the first freezing and 6% for the second one.

Despite of the undrained system, a 4% reduction in frost heave is observed.

As shown in Figure 7.18, water in free state exists between the sample and the membrane

after thawing. An hypotesis is that the water particles are less bond to the soil particles, or even

they get free. This might lead to think that its freezing temperature is increased. Since the system

is undrained, more water in free condition exists for the second freezing. According to this, a

larger amount of water will freeze at the same bottom temperature than the previous freezing,

recording then an higher frost heave.

Since the above hypothesis were not confirmed, an analysis in terms of diameter was realized

in order to see if the real frost heave reduction was hidden behind a change in section.

The diameter of the cross section along the entire sample (70 mm in height) was measured

when soil was in unfrozen state, at the end of the first and the second freezing and at the end

of thawing (Figure 7.20). The diameter measurement was under the hypothesis of circular cross

section along the entire, despite of the deformation process is three-dimensional. The explanation

of each curve is in what follows:

76


1. in unfrozen condition the sample has a constant 70 mm diameter, but at the top and bot-

tom, probably due to sample handling during its preparation and x-ray artefact (since the

closeness to metal cups);

2. at the end of the first freezing we see a global reduction in diameter along the height of

the sample, which slightly increases ahead the frost front. At the frost front the minimum

diameter is measured, telling that the denser zone develops almost at the same elevation of

the frost front;

3. after the end of the thawing the diameter becomes less than in the unfrozen state in the upper

zone. The difference in size is due to the redistribution of water from the upper zone to the

bottom. Since no increase in diameter is observed in the bottom zone, the specimen does

not absorb such water but it leaks out and gets trapped between the soil and the membrane.

4. At the end of the second freezing a large expansion in section at the bottom is visible, while

the diameter at the frost front is smaller than in the first freezing.

As Miller (1972) explained in its ”Secondary frost heave theory”, frost heave does not exist

just due to the expansion of water but it is also the result of its slow redistribution though the

partially frozen region of the soil due to the existence of a premelted film of water at lower

temperature than the freezing one. On this basis, one may say reduction in frost heave occurred

since redistribution of water was not accentuate as the previous freezing. Indeed, due to the freeze

and thaw, a great amount of water is already migrated downwards and a part of it changed its

status from bond to free water. Such conditions lead to a water demand by the bottom part to the

zone above which is satisfied with a less amount of water than the previous freezing. Cryogenic

suction acts also on the free water already existent in the bottom zone, which is suck into the

specimen and frozen, involving in an increase in diameter.

Furthermore, the diameters analysis allowed to see that the freeze-thaw process is reversible

in the bottom zone, since the cross section diameter takes back its size.

77


Figure 7.16: Specimen’s vertical section inunfrozen state

Figure 7.17: Specimen’s vertical section atthe end of the first freezing

Figure 7.18: Specimen’s vertical section atthe end of the the thawing

Figure 7.19: Specimen’s vertical section atthe end of the second freezing

78


Figure 7.20: Diameter along the height specimen for four different instant

79

Chapter 8

Frost front penetration prediction

Prediction of frost heave and frost front penetration is critical in cold regions civil engineering.

Infrastructures, buildings and foundations are always under damage risks by frost heave and

thawing settlements and millions dollars are spent annually on their preservation and restoration.

Since 1960s, several sophisticated models are developed in order to predict frost heave and frost

front penetration in soils. Groenevelt and Grant (2013) identified two principal ”schools”. The

fist is the school of D.M. Anderson of the Cold Regions Research and Engineering Laboratory

(CRREL) in Hanover, New Hampshire. The second is the school of Bob (R.D.) Miller, of Cornell

University, Ithaca, New York. Over the years, new schools are born and new refined concepts are

continually introduced to the ancient theories in order to obtain a better prediction of behavior

frozen soil. Such theories have often foundation on equilibrium thermodynamic concepts (e.g.,

Clapeyron equation) and use hydro-dynamics (e.g., Darcy equation) and mechanics notions.

8.1 Stefan formula and Modified Berggren equation

Despite of the existence of several sophisticated model in literature, frost front prediction is

usually realized by manually applying simplified equation for Infrastructure Engineering. One

of the first and simplest equation proposed for this scope is the Stefan Formula.

On the hypotesis of 1D freezing, Stefan formula assumes that the latent heat of soil moisture

is the only heat which is removed when freezing the soil. Thus, the thermal energy which is

stored in the form of volumetric heat and released as the soil temperatures drop to and below the

81

8 – Frost front penetration prediction

freezing point is not considered [Aldrich Jr (1956)]. The assumption of volume heat negligibly

involves in the overestimation of the frost front penetration.

The Stefan formula states that the heat conducted to the ground surface through the frozen

layer, expressed by the Fourier’s equation (left term of Eq.8.1), is equal to the latent heat released

by a layer of soil dx thick in time dt, expressed by the conservation of thermal energy, in which

the volumetric heat is neglected (right term of Eq.8.1).

k fdTdz

= Ldzdt

(8.1)

where k f is the thermal conductivity,vertically measured in the frozen soil from the ground

surface and L is the latent heat of water Lw inside the soil, computed taking into account the soil’s

water content w and its dry density ρd (eq. 8.2).

L = Lwwρd (8.2)

By integrating and solving for z, one obtains:

z =

s2k f

L

Z t f

0(TP − TS )dt (8.3)

in which TS is the temperature of soil surface at depth zS = 0 m depth. TP is the temperature

at the frost front depth z, unknown of the problem. t0=0 is the initial time of freezing and t f is

the period of freezing. The termR t f

0 (TP − TS )dt corresponds to the Surface freezing index (SFI),

usually expressed in days Fahrenheit or days Kelvin. It is also possible to use the Air freezing

index (AFI) by adding a coefficient n, depending on the kind of layer above the soil surface (for

instance snow, concrete and bituminous mix). The AFI is expressed as the SFI but it consider the

air temperatures over the time.

In this was Eq.8.3 becomes:

z = 416

rk f nAFI

L(8.4)

Due to the overestimating trend of the Stefan equation, several modifications were proposed

for it, over the time. Noways, design of pavement structures in cold regions is realized on the

basis of the (UFC), which proposes to use the Modified Berggren equation (Eq. 8.5). This last

82

8.2 – Experimental data and model results comparison

corresponds to the Stefan formula corrected by introducing a corrective parameter λ, obtained on

the basis of thermodynamic theories.

z = 416λ

rk f nAFI

L(8.5)

The parameter λ depends on the volumetric heat capacity, computed as the average between

that of the unfrozen soil cu and the frozen soil c f (Eq.8.6) , on the latent heat of water iside the

soil L and on the surface temperature TS and freezing temperature of water inside the soil TP by

the parameters µ and α, expressed in Eqq.8.7 and 8.8. In Eq. 8.8, Tm is the recorded maximum

annual temperature in the zone. Once computed µ and α, λ is calculated from the graph in Figure

8.1.

cavg = ρd(c + 0.75w

100) (8.6)

µ =cavg

L(TS − TP) (8.7)

α =Tm − TP

TS − TP(8.8)

8.2 Experimental data and model results comparison

In order to realize a comparison between experimental data and frost penetration model results,

the −12 ◦C 1D freezing case was considered. The Stefan formula expressed as Eq.8.3 was ap-

plied over the time, considering the temperatures 0, -3, -4 and −5 ◦C as frost front temperature.

The sample’s metal bottom cap temperature recorded by thermocouples was considered as soil

surface temperature TS .

The thermal conductivity k f , was computed as the average between the one of the frozen soil

and that of the unfrozen one. The values were that measured for a clay sample by Kurz et al.

(2017) and its properties are in Table 8.1 and they are equal to 1.21 and 0.90 W/mK for the frozen

and unfrozen clay, respectively Following such procedure, the graph in Figure 8.2 was obtained.

It shows The better interpolation to the experimental curve was obtained for -3 and −4 ◦C.

83

8 – Frost front penetration prediction

Figure 8.1: Correction coefficient in the modified Berggren formula from Aldrich Jr (1956)

Table 8.1: Plastic index Ip, saturation degree S r, natural water content wn and dry densityt γd

measured for a clay sample by Kurz et al. (2017)

Ip S r wn (Mg/m3) γd

24.2 85 36 1.3

The Modified Berggren equation was applied just for the last freezing instant (700 min), com-

puting the SFI as the integral of all the temperatures recorded untill that instant and λ for the

temperature TS recorded at 700 min. By using the Modified Berggren equation all the frost front

position predicted by the Stefan formula are reduced of few millimeters (Table 8.2).

The carried out analysis allows to say that the usual hypothesis of 0 ◦C temperature at the

frost front involves in an overestimation of frost front penetration. This was already observed in

literature for the Stefan formula. For 0 ◦C case, also the Berggren’s λ parameter is not sufficient

to match the experimental data. Contrary to the current practices, for the short-term clay freezing

better results are obtained by applying the Stefan formula and considering that the freezing tem-

perature, which corresponds to the temperature at the frost front, is actually some degrees below

zero.

84

8.2 – Experimental data and model results comparison

Table 8.2: Frost front position after 700 min −12 ◦C freezing by Stefan formula and ModifiedBerggren equation

T (◦C) 0 -3 -4 -5Frost front (Stefan) (mm) 71 61 57 53

Frost front (ModBerg) (mm) 68 59 56 51

Figure 8.2: Frost front penetration over the time by Stefan equation for 0, -3, -4, −5 ◦C TP

85

Chapter 9

Conclusion

During this master project several freezing procedures were investigated in order to find the one

which returns an elementary representative frozen samples, homogeneous and isotropic. The

required characteristics were uniformly distributed ice crystals and small in size respect to the

soil matrix. In the way they cannot be identify as a separated phases from frozen soil.

First different sampling procedures were tested. Difficulties have been identified at this step,

since the returning of air bubbles in the clay sample by using the sampling techniques explained

in literature. Air bubbles affects the freezing process since they corresponds a preferential loca-

tion for the initiation of ice segregation. Furthermore, recent study have revealed that water can

infiltrate into deeper soil through preferential pathways where air-filled macropores exist at the

time of freezing [Niu and Yang (2006)]. After some trials, the introduction of concrete vibra-

tor in the clay slurry before consolidation was believed a good improvement for the specimen

preparation, since it returns less air bubble porosity than the other methods tested (Figure 4.8).

During the three-dimensional freezing campaigns, two kind of soil were tested: Halden silt

and Onsoy clay. In the Halden silt ice crystals were not identifiable by a 60 µm resolution x-ray

tomography. Hence, it can be concluded that a reliable mechanical response of an Halden silt

frozen specimen could be obtained by almost any freezing procedure.

For the Onsoy clay, ice crystals have been noted when the temperature drops below −4 ◦C.

Three main factors were observed affecting the average of ice lenses thickness: the freezing

temperature, the water content and the rate of freezing. Finally, among the freezing methods

tested during this master thesis, the slow freezing to −5 ◦C was identified as the best procedure

87

9 – Conclusion

to freeze, since it involves in the most homogeneous and isotropic soil material.

Two one-dimensional freezing campaigns were carried out. The cold was imposed at the

bottom of the specimen.

During the first campaign, Halden silt and Onsoy clay one-dimensional freezing was com-

pared. For the Halden silt, a net frost front was seen moving upwards without ice lenses devel-

opment. Ice lenses grown in Onsoy clay and a three-dimensional deformation behaviour was

observed despite of the one-dimentional freezing. Further analysis were carried out about the

change in density and strains along the height of sample due to the imposed thermal gradient.

Four different zones were identified where soil differently behaves.

For the second campaign, three different thermal gradient was imposed to the specimen and a

freeze-thaw-freeze cycle was observed. Thermal gradient affected the deformation of the speci-

men. For this case, the analysis were focused on the quantification of the frost heave and the

maximum frozen height. They were measured greater for lower bottom temperature. Frost

front elevation increased at similar initial speed for all the cases and then it tends to stabilize

(equilibrium-steady state) (Figure 7.13).

After one freeze-thaw cycle water was observed leaking out from the sample. It appears

trapped between the membrane and the soil in Figure 7.18. After one freeze-thaw-freeze cycle

frost front elevation and frost heave was measured less than after the first freezing. Furthermore,

the equilibrium-steady state was reached in shorter time for the second freezing than for the

first one. To further investigate this phenomenon, a diameter analysis was carried out. A global

reduction in diameter was observed along the height of the specimen after the first freezing. The

thawing induced sample’s cross section to retake almost the initial diameter in the bottom zone,

while in the upper zone the diameter keeps smaller than in the unfrozen state. After the second

freezing, diameter increased above the one measured in unfrozen state, while it keeps smaller in

the upper zone.

Results obtained during the second one-dimensional freezing campaign were applied on ex-

isting method for the prediction of the frost front penetration. Two equations were used: the

Stefan formula and the Modified Berggren equation. The experimental results obtained for one

case of freezing were well matched by the Stefan formula during the freezing period. In particu-

lar, a better interpolation of the experimental data was noted considering -3 or −4 ◦C as freezing

temperature of water inside the soil. The Modified Berggren equation returned an overestimation

88

9 – Conclusion

of the frost front position after 810 min freezing.

X-ray tomography was critical for the understanding of the freezing process and the detec-

tion of short-term deformation. The digital image processing has been found an innovative and

important instrument in the frozen soil analysis. Indeed, it gives the tools for the quantification

of phenomena of which just qualify explanations exist in literature. For this reason, it would be

a worthy ally for the improvement of constitutive model already proposed in literature. Further-

more, linked to mechanical test apparatus, it would improve the interpretation of the mechanical

response of the frozen soil. Finally, it could fill the gap existent in the current body of knowledge

regarding the phenomena involved by the freezing of soil and and the influence of freeze-thaw

cycles on the soil physical, mechanical, hydraulic and thermal properties.

89

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